#geometry-and-trigonometry
1 messages ยท Page 340 of 1
i am having a geometry problem
imagine u have a picture of 320x320 pixels
and i wanna put inside another picture (square) that can be anything randomly between 150 and 200
what are the coordinates (top left corner) to spawn the small square regarding the big picture?
idk if i explained myself
On X axe i though about
x = random.randint(50, dims[0] - s - 50)
the 50 is just a small offset
dims = [320, 320]
ands is the scale factor
s = random.randint(150, 200)
But on y axe i want the to spawn from the mid to the bottom
i dont want the on the top
nvm, i did
?
If I have the value of sin(theta), how would I use that to figure out cos(90-theta)?
Yes?
Can you help a brotha out
lol
Thank you
yep
can anyone kindly help with this
whats the width if the length is 3x more than the width and the perimeter is 80
<@&286206848099549185>
it is 3 am and i have an headache
Find the area of the two sectors
and just subtract em
Oh, I already worked it out lol
forgot the equation for the area of a sector

lmaooo
rookie error, but thanks

$x \cdot \sqrt{2} = \frac{{18\sqrt{2}}{\sqrt{2}}}$
Skyler
Compile Error! Click the
reaction for more information.
(You may edit your message to recompile.)
Uhm
Can somebody help with that?
It is supposed to be 18 times the sqrt of 2
over the sqrt of 2
should be \frac{18\sqrt{2}}{\sqrt{2}}
Ah , so the suffix or /frac does not requre a bracket ?
Man , this reminds me of C++
$x \cdot \sqrt{2} = \frac{18\sqrt{2}}{\sqrt{2}}$
Skyler
i dont think that is readable ๐ค
Oh noes
let me write something rq in html
<html>
<head>
<p style="text-color:red; font-family:times new roman;"> Maths(idk)</p>
<title>
Math
</title>
</head>
<body style="text-align:center; text-decoration:none; font-color:234211">
</body>
</html>```
Something like that ^
Ah more like this
This is not mine , but it's in VSC
I use vsc
Oh sweet he is using LoRa
Wait ? I think that's an uno
hooked up to a LoRa gateway for long distance messages ???
Hey, I got this question on a practice paper. I got x=360n where n is 0,1,2... and -1,-2... which seems to check out okay and satisfy the original equation. The official answer (in the image) includes this solution (apart from the negative values for n) but it also has two other solutions which don't even satisfy the original equation exactly. Have I done something wrong or would you say there was an error with the official answer?
I need help
help PLEASE
@lusty slate that isnt geometry
@dire notch im guessing thats an equilateral triangle even tho it kinda sucks that they dont even tell u
so 3x-7 = x^2 - 17 = x+4
All 5
hmm
well initial means starting value
so i mean what would the initial value be
@lusty slate u gotta answer me if u want this to get done
we are starting w number 2 btw
bc ill save number 1 for last
well ill save it for after number 3
so ur trying to say that angle 1 is angle 4?
hmm
well u can problem solve thru tihs actually
so 3=4 right?
XW bisects VXY so 3 has to be 4
and since XS bisects RXT then 1=2
and 2=3 is a given
so if 2=3 then 1=3
and if 1=3 then 1=4
and boom there u go
Yes!
I was thinking about a problem my professor had done, where given the points of a vertex he starts demonstrating part by part until he gets to the angles I need to demonstrate.
Ok, I will check the theorem again.
there is another similar exercise I'll try to solve it.
ok
Hey i hope this chanel is free
Can somebody explain the steps how to simplify the expression ? I have no idea
hmm
i mean i would think its just sin^4(x) + sin^2(x) cos^2(x)
but there must be something else to it
Yeah thats what I thought too but apparently thereโs gotta be neither way
Consider looking at both terms, notice that both have something in common
sigh
fck
cos
jajaja
@upper karma please don't give away answers. It doesn't help them learn.
I see, thank you๐ ๐
sin^2(x)(sin^2(x)+cos^2(x))?
Yeh
my error F
sin^2(x)+cos^2(x)= 1
sin^2(1)
sin^2
Still not good.
That's nonsense
Ooh, I'm an idiot point I II and III, is the thesis.
Would this be ok?
Hi, I am doing this exercise and it tells me that <1=<4.
I say it can't be the same, it should be <1= <2+<4
Am I right?
1 isnt 4
it cant be 4
visually you can tell, and with the info given too u can also tell
"No, in fact, <1=<4.
You see, we have that, both angle BCH and EAB are flat, that is, they measure 180ยฐ, so, let's make <2=<3=a, <4=b and <1=c, so that <BCH=a+2c and <EAB=a+2b, but <BCH=<EAB, since both are flat, then:
a+2c=a+2b, then 2c=2b, so that:
c=b, that is, <1=<4."
I asked another person and he replied this.
according to what you told me and seeing the graph visually I do not see the equality either, the truth
ScapeProf
its not 4
its 2 ?
so would it be
$x = \frac{18\sqrt{2}}{\sqrt{2}} = \frac{18\sqrt{2}}{2} = 18?$
Skyler
uhm
no the answer in the end was correct
$x = \frac{18}{\sqrt{2}} \cdot \frac{\sqrt{2}}{\sqrt{2}} = \frac{18\sqrt{2}}{2} = 9\sqrt{2}$
Skyler
yep
Thanks
Are you an ASDF potato ?
That reminds me of this crappy meme i used to know in like 3rd grade
angles 1 and 4 are the same from the information provided
it says CF bisects BCD, which means his a+2c is correct
Ok thanks โค๏ธ
no worries, np
๐
sorry i have to do some stuff for robotics
i cant help u for now maximo but i bet u can find someone else
Thanks bro, no problem :''3 โค๏ธ
Hi guys
one questions
Daum Equation Editor has just been closed, what other site do you recommend for my reports please !!!!
Can someone please help with 11?
Sum of any 2 sides of a triangle is greater or equal to the other side
thanks guys preciate it
gotta mention helpers @modern estuary
not to mention ur name is annoying to mention
i could help u tho
well im going to bed rn
hmm
๐ธ
F<A btw
k thanks
these is isosceles
triangles
Smbd rq
atlest tell me what to do for it
yo do you know how to solve this
thanks man im not gonna lie that was great advice
All of the triangles are similar
which means the proportions between corresponding parts are equal
they have pair of congruents side and 2 pair sof congruent angles
one of them being b as a reflexdive
Isn't there more than one
Hey I really need help with this one, AD, BE and CF are medians in triangle ABC and they intersect in G. AD perpendicular BE. AC=10cm. โ AFC=86ยฐ. CG=AB. I need to find the length of AF. I got stuck for a full day trying to do it
How plss help
hint: diagonals of a rectangle are congruent and bisect each other
I Need To Solve For Each Missing Variable But I Don't Know The Formula Or Where To Start
For Number 5
@upper karma dont think of them as quadrilaterals
try and imagine if you could extend those parallel lines
So Would I Do 360=6x+10+2x+10
is that what all angles add up to
Yeah
i think you'd have to do 360= 2(6x+10) +2(2x+10)
Alright Thanks Couldn't Get Past This
Result:
340
340 doesnt equal 360
could i please get some help with this problem
distance formula
choosing the side with the simplest values for less tedious calculations
you are told that the heptagon is regular
so you can multiply that value by 7 instead of applying the distance formula with crappy values 6 more times.
thank you ๐
need help with these 2.
nevermind i figured out the first one, i got C. i just need help with the 2nd now.
the 2nd question is considerably easier than the first
nvm im watching youtube tutorial i did them both i just forgot the formula
well actually its about the same amount of work
pls no direct pings in the future.
draw a diagram, apply the definition of bisection.
can you divide it to seven triangles and get it from there?
why would you need to divide it into 7 triangles
i mean
you can make 7 right triangles
with each side as the hypotenuse (longest side of the triangle)
and then solve using the pythagoras theorem
all of that I just said is just rephrasing the distance formula
so guys is there a chance that this is unsolveable?
yep
I dont think it is unsolvable
but im not sure where to start
I Don't Understand What I Have To Do For 2 Because When I Do 2x+15=X+15 I Get 0 Which Doesn't Work
yeah, x = 0 is right
But What Then ST Is 0 Which Doesn't Work If I'm Right?
WAIT
NEVER MIND DUMB BRAIN MOMMENT
the sum of the lengths of the height and the edge of the base of the hexagonal pyramid is 10, the axial section is 48, Find the area and volume
,rotate
i need help
A brief description and guide on how to use me was sent to your DMs!
Please use ,list to see a list of all my commands, and ,help cmd to get detailed help on a command!
i also need some help๐
i am pretty new to geometry
and i cant solve this question
what question
๐ป
@silk briar ?
im drawinh it on geogebra
this is the picture
and i have to solve the are of the big half circle
the area of the big semicircle...
is anything else given other than that chord marked as "2"?
no ๐ฌ
then there is not enough information i'm afraid
our geometry teacher just drew this during the class and said tthat we have to solve it
oh he also said that the chord is in 90 degree angle with the diameter
i could see as much, given that it's tangent to the two smaller semicircles.
did he not say anything about those smaller semicircles by the way?
no
then this problem is impossible.
by varying the size of those semicircles i can make the big one have many different sizes.
oh!
this...
changes everything
wait.
is the vertical chord's length meant to be a+b?
is that what you constructed/assumed yourself?
yes
because that would make the chord a radii which seems like its not supposed to be
perhaps you were actually asked to calculate the area of the red region
which would actually be possible

sorry for that
assign variables for the radii of the smaller semi-circles
express the radius of the larger circle in terms of those
then subtract areas of the smaller ones from the largest semi-circle
that would be the first part
you can get more information about your radii by applying something like intersecting chords theorem and/or otherwise
and you should end up with a constant
should i use proportion with it?
use a proportion how?
yes
and then you're 1 step away from your answer
yes
Providing instructional and assessment tasks, lesson plans, and other resources for teachers, assessment writers, and curriculum developers since 2011.
What
ok
Hello, could someone help me with this exercise pls.
x=40
hey guys
how do i calculate the trigonometric functons without information on other angles or sides?
in a question i got for a quiz the question tan1 + tan2 + tan 3 + tan4 ... + tan88 + tan89 appeared and i don't know how to solve those kinds of trig
pweese <@&286206848099549185>
PLEASE I NEED HELP <@&286206848099549185>
that question seems to be too complicated for your current understanding of trig functions
Does anyone know how this is done
Did you solve for AE?
@green tree @hybrid solstice
@upper karma That's solved by equality of proportions.
How do I solve volume of sphere without Calc
Err, I wonder if that's possible.
You mean* deriving 4/3 ฯrยณ from scratch, right?
I guess in the old days what they did was got a heavy ball, dumped it into water and saw how much the water level rose.
@upper karma I found an interesting site called gingersnapmath wordpress that shows a derivation of the volume of a sphere using the geometry of a cylinder and a cone. Might be what you're looking for.
@tropic shard --> isn't the formula there from Archimedes days? And he didn't know Calc
It is, he's quite the smart, legendary philosopher
no
is advanced trigonometry by durell a good book to self-study trigonometry?
i want a somewhat rigorous treatment if that is possible
I know this is a parallelogram, but i am wondering if it could be a different shape, where could I start to find out
Hey, when verifying trigonometric identities, is it possible to use 1 + tan x = sec x as a Pythagorean identity as opposed to 1 + tan^2 x = sec^2 X?
No
cause 1+tan = sec and 1+tan^2 = sec^2 arent the same thing
how do we determine that an angle bisector of the angle formed by two intersecting lines is an acute- or obtuse- angle bisector?
sqrt of 1+tan^2 isnt 1+tan
it's secant of that angle...
Since the line starts at the origin, y intercept = c = 0
m = 2
Substitute that in y = mx + c to get y = 2x
Use distance formula for a point from the origin [sqrt(x^2 + y^2)]
So u have x^2 + y^2 = 2645
Now solve y = 2x and x^2 + y^2 = 2645
Consider only + values as graph is in quadrant 1
cause im no sure if im correc
Ans is 23,46
how do you find the sides of an isosceles triangle given 3 angles
why is radian part of trig
<@&286206848099549185>
3 angles alone is insufficient to determine the sides of any triangle
given an area also whixh is 36 sq m
apply trig formula for area of a triangle
How do I type this in my calculator
depending on your calculator, you may have a \
$\circ$ ' " button
โamonov
its for degrees minutes and seconds
k
k ty
also make sure your calc is set to degrees
Is there something wrong with my calculator? I am new to Sin, Cos and tan and when I enter tan 45 it is supposed to be 1 but when I enter tan 45 in my calculater I get 1.61977... why is this?
Will I have to change it back for normal calculations? Or can I keep it in degrees mode?
you can keep it in degrees mode
Thanks a lot ๐
just choose the correct mode depending on the units in the question
But it only effects it when you use sin, cos and tan?
where are you stuck?
order of operations please
@short grail
assuming you recognised you have intersection chords and are attempting to apply the related theorem,\
$x-2(9)$ is NOT the product of $x-2$ and $9$ \
$x-6(15)$ is NOT the product of $x-6$ and $15$ \
โamonov
can someone help me with this
$\sin{4.76^{\circ}}=\frac{4}{\textsc{carpet length}}$
jolimath
The 26-deg doesnโt matter. AC is twice the length of DF because itโs the segment joining the midpoints of AE and CE. The answer is 12.4
honestly i just started geometry and im already so confused, i tried my best to pick things up but i cant really wrap my head around it, could anyone assist?
ive tried looking at some online resources but i dont really pick things up the best with those types of resources and would rather have someone right here to help me out
its been quite a while since ive had a math class, it was a year and a half ago when i had algebra and i forget a lot of terms easily
I just started geometry with the new semester
can someone also help me
scratch that figured out the first portions ill use the help channels if i have questions
can someone please help me with this
๐
thanks
what is the way to setup the equation
The area of a trapezoid is 60. The length of one base is 7 units greater than the other base, and the height of the trapezoid is 5. Find the length of the median of the trapezoid.
i dont understand anything lmao
Would it be fair to say that, since "two lines can intersect at one point at most," directly implies that "two planes can intersect along one line at most"? I can't see why it wouldn't be true but wanted to get some thoughts before I settle on that answer
reasoning just being that planes can be thought of as linear extensions of lines into another dimension, so the path they trace through space forms a plane, and the point they intersect traces the path of a line
i have a question....
damn fr
@unreal patrol you can use the hint above.
Have you tried anything so far?
nop
Well, start by trying something out considering you have all the trig identities you can use to manipulate sec(A/2) into something you can find easily.
If you get stuck let me know.
It says "test" on the title.
<@&268886789983436800>
@worn folio hi. Delete dis
ty
@worn folio well I did it on your stead
given that you were doxing yourself by asking help for that test
never ask for test solutions
@upper karma ty as well for the notification
How do
@upper karma Im in Cp geomotry, and my teacher uses General geometry tests for our hw lol.
I dont want to have to wait to consult my tutor after school
cause then it turns into an hour of studying spanish after the one part of math
my brain hurts can some one help me
i just need the equation
this is proportions
it wouldnt
why did that statement warrant a "but"
Hello, may i ask some help about solid geometry? frustum of a cone to be exact.
"can I ask something?"
doesnt ask
if you were given a product of radius of bases in a frustum, how do you get each radius if the given is height, volume and the product of radius?
I mean the height of frustum, volume of frustum, and the product of the radius of the bases of frustum...
Apply the formula
The volume formula
then substitute
the product
so if the product is xy
suppose 50
x=50/y
then plug this in volume formula
Good
hey guys does anyone know how to use the unit circle
i havent payed attention during the last few months n we are doing a quiz review
@scenic glacier
for number one its asking what angle makes cos = -1
think of cos as your left and right and your sin at top and bottom
or you can think of cos as your x and your sin as your y
@graceful totem when you have a sec do you think you could help me with this?
Hello
can someone help me plz
sure
ok thx i need it
hmm
im not too good at geometry
but i think it might be talking ratios?
maybe
ok @sacred geyser so this is a ratio thing
the geometric mean is the ratio of the shorter leg (KN) to the longer leg (LN)
and if you broke that triangle into two triangles,
their altitudes would be the same
could someone please help me with this problem
i do not really know where to go from this
i made some isoceles traingles and found that x/2 = 90 - <OCB
what is NP and NL
AD=(1/2)(BD)
@worn folio use the triangle midsegment theorem
@worn folio google the triangle midsegment theorem and use that
Dunno why I am getting really off answers someone double check for me and tell me if it is a parallelogram (this doesnโt cheat I gotta show work)
<@&286206848099549185>
Desperate deadline midnight for progress reports
Hi, can someone explain the intuition here behind dividing every term by cosacosb?
To turn everything into a tan term
ah gotcha
How do I derive the right hand side?
deriving cos(2x) = cos^2x-sin^2x is pretty straight forward
dont know about the one in the picture
same with this one
the lecture notes didnt actually explain how they got these
they just told us that these are also identities
have you seen the pythagorean identity $\sin^2(x)+\cos^2(x)=1$?
Sneaky
:)
โค๏ธ
so I guess there's no easy way of deriving 1-2sin^2x directly from cos^2x-sin^2x right?
its mainly just a matter of knowing the pythagorean identity?
not without pythag identity lol
but pythagorean identity is everywhere
you won't be forgetting it
no worries
tangent would be enough
Thank you!
you'd need to fix #2
just points on the circumference
Is it possible for someone to help me with 10 pages of unit 6, lessons 1-5 of geometry? The unit is called relationships with triangles.
is that better
The only problem is that people will likely not want to do 10 pages of work
understood
If your question has not been answered for a minimum of 15 minutes, you may use the Helpers tag once. Please do not try to bump your question using this ping unnecessarily. Do not abuse this ping. Do not individually ping users with the Helpers tag without their express permission.
@pseudo bison do you still need help?
note: blah blah
Me: draw perpendicular ๐

Have you heard about arcsine?
no
Well here's one hint
As the two shorter sides form an angle that approaches 180 degrees, the third side's value approaches the addition of the two shorter sides
So essentially, if the third side is greater or equal to the two shorter sides, then a triangle cannot be made, because the triangle's value would essentially need to be > 180 degrees, which is of course impossible
and that even if side one and two were to be parallel to each other, they would not be able to connect with the third side end by end
I'll start off by stating some theorems
The sum of the areas inside a triangle is always 180ยบ
therefore if you know two angles
you can find the other angle
thanks man
Anyway, so
so for the first one
wait mb
mb i meant 180 instead of 120
you do 180 - (108 + 29)
= 180 - 137 = 43ยบ
so the angle under D should be 43ยบ
Alright. So the next theorem is
how the hell do you do that.
geogebra
HAHA
if two points on the circumference of a circle
have a common chord
they're the exact same angle
which means that ......?
@upper karma
TOS 
*angles
Hi, how do I find out if this is a cosine or sine function?
yes, although you could simplify it to 2+sqrt(3) by rationalizing the denominator
@cloud meteor same arc bro
Need some help
You can check using desmos
Just make sure you're in radians
Good question
basically the diagram
does it click now?
shift the perpendicular to the side
the radius of the smaller circle adjacent to the bigger circleโs radius
shown in dotted lines
now pythagoras theorem
The values are given
Create an equation
nice done
what have you tried?
no
wow I am terrible
going back to the one I was talking about. . . what trig ratio did you use?
what trig ratio did you use
sin
right, 17.976 is right
did you draw a diagram?
yes
what trig ratio do you use?
tan?
no you dont know adjacent
oh so sin?
yes, then add on how high the triangle would be off the ground
and I would put 540 in as the hypotneuse right?
yes
wouldit be 536?
or 537
yeaaaa it would right, cuz last time I subtracted 36 instead of adding it
thx a lot @humble pulsar
For trig, is the ratio of tangent cos/sin or sin/cos? I forgot
sin/cos
cot is cos/sin
omg ty ๐
1/2 x is just half of x
1/2 is just a number
so do I disregard it?
Sorry I'm still not following ๐
1/2 x is 1/2 multiples of x, (1/2)x, x/2 or however you want to view it
just like how 2x is 2 multiples of x
3x is 3 multiples of x
etc
So it's just 1?
wdym
Subtract add etc.
ok.
well technically you don't even need to apply it because the question is over specified,
but this seems like a real issue you need to get past
what does it mean for a triangle to be equilangular?
those are angles,
but yes as a result all the sides would be the same
and apply that
for the purposes of dealing with 1/2 x
set XZ equal to either of your other 2 sides
e.g XY
and you'll get the equation:
$2x+10 = \frac{x}{2} + 28$
โamonov
and solve that like any other equation
O
Ok thank you
Basically set
XY and YZ to be the same
which makes solving XZ easier
you can set any pair of sides to be equal and solve for x
XY = YZ will result in the easiest calculations
you can sub your value of x into all 3 sides to double check your answer and the question is actually valid
identify corresponding vertices and apply distance formula
How would I go about doing that
be familiar with congruence notation
Guys
how could I know if the norm of any of these vectors would be equal to
the norm of this vector
I know the norm of the vector v is 1, but don't know how to see the norms of the others vectors
Hi, how do I know if I should write this as a cosine or sine function?
This is what I have so far, I'm just not sure if I should write it in terms of cos or sin
@upper karma what's e1,e2,e3?
heyy i got some questions and i think this is the right channel for this type of math maybe
@lusty slate 4m = 4000 mm
300 mm = 30 cm
234 mm = 2.34 dm
@lusty slate look up metric conversions
A sinusoidal function with an amplitude of 15 units, a period of pi/2, a phase shift of pi/7 radians to the right, axis at y =33
This is my answer: y= 15f[4(x-ฯ/7)]+33
Is f cosine or sine? How do I know?
Thanks
@idle bobcat i'm guessing that "axis at y=33" means it touches the y-axis at y=33, then consider what occurs when both functions cos and sin are at x=0
How would I get the radius of the inner circle? I know the perimeter would be 6R
would it be sqrt(3)/2 * R ?
I guessed that from the options I got
Good question
Iโll give some hints
You can divide the hexagons into isosceles triangles
Then the median
Would become the radius
and the pattern continues
axis just means the midline
I'm just not sure if I'm given a question like this how I determine whether to use cos or sin for my function
usually, it tells me whether its sine or cosine, and I just need to put together the rest
i think the answer should be (4x-pi/7). Not 4(x-pi/7)
technically, cosine is just sine with a phase shift of pi/2. so i think u should answer with sine
this is the answer imo: 15 sin[4x-ฯ/7]+33
can u elaborate on why?
because it says the period is pi/2
and 2pi/(pi/2) means our k value is 4
wouldnt you need to distribute that value to pi/7 if you wanted to express it the way you did
but the thing I'm confused about with that is sine can also just be a phase shift of pi/2 to the left of cos cant it? so how do I know if the function is a base cos function shifted pi/7 to the right, or if it's a base sin function shifted pi/7 to the left?
usually in these problems they either explicitly tell me to write it in terms of sin or cos, or they atleast give me hints in terms of what the y axis intersects, or some other related hint
yes. even my answer has a period of pi/2. The only difference btw my ans ans urs is the phase shift
by convention, sin(ax+b) has a phase shift of b
so if u want a phase shift of pi/7, b must be pi/7
yeah but in your equation you brought the k = 4 value inside the brackets
which means you would need to distribute
yea you're right there. it can be cos also. the question must have mentioned clearly
yes, the period doesnt change after u distribute
try plotting both in desmos
y=af[k(xโd)]+c this is the general form I was taught to use
so if you bring the k into the brackets, you would need to distribute the k to the d
yea you would. but the period doesnt change bcos of that. the coefficient of x is the **only **determinant of period
yeah bro but the period is still pi/2
im saying the d value would change
ok i misunderstood
.
nope, they gave no hints or anything
what im telling is, if u want a phase shift of pi/7, k*d must be pi/7
and not d=pi/7
idk if they taught u that d is phase shift
the general convention is k*d=phase shift
then dont worry about f. it can be both sin or cos
ok if this is what they taught u, go with it
in electrical engineering, k*d is phase shift
ok yeah so anyways, how can it be both sin and cos?
but go with your textbook
because they both give different graphs
yea but the question hasnt mentioned it clearly right
yeah
so both should be accepted
ok so I guess I was right that there wasn't enough information
in order to determine whether they want sin or cos
yepp
ok yeah I was confused for so long about this question..
do you know the simplest 30-60-90 side lengths?
No
I have no idea how to do that ๐
have you tried anything?
ok well can I see what you have tried..?
Can't access it anymore
Do you know what this type of math is called
GOnna see what I can find on Khan academy
Trig...
this is a 30 60 90 triangle
it's a triangle that has one 60ยบ angle, a 30ยบ angle and a 90ยบ angle
don't mind the thingys on the sides of it
draw one of these
and that bigger side
the hypotenuse
make it 16 cm long
then
you see the side that's the opposite of the 30 degree angle?
it's the opposite side to the 30 degree angle
and the adjacent side to the 60 degree one
you'll need that, but height first
that you can solve by doing this:
sin 60= height/ 16
so height will be sin 60 * 16
then the base
is
sin 30= base/16
so base= sin30* 16
then to calculate the area you do
base*height all dividing by two
there u go
@upper karma
i'm learning trig now, this was the easiest way i found to explain it, excuse me if it ends up being wrong 4
So uh I was thinking about how the graph of sinh looks nothing like sin, but does somewhat resemble tan. It's kinda like a stretched out version of it
The same can be said about cosh and sec
And not only are they both stretched out, but they're stretched out by the same amount
So if sinh(x) = tan(y), then cosh(x) = sec(y)
This is not so hard to see given the identities cosh^2(x) - sinh^2(x) = 1 and sec^2(x) - tan^2(x) = 1
What I noticed is that every hyperbolic function can be viewed as a regular trig function cut off at +/- ฯ/2 and stretched out to infinity (by the same factor)
tanh is sin stretched out
sech is cos stretched out
csch - tan
coth - csc
And they hv identities similar to trig functions
Maybe this is the reason for the similarities
All identities that don't change the argument are analogous as far as I've seen
if sinh(x) = tan(y), then cosh(x) = sec(y)
And this holds true for all pairs
Though signs are a bit tricky with the even functions
๐
To take it a step further, since e^x can be written as sinh(x)+cosh(x), it's "squished" version is tan(x)+sec(x)
Which means that the squished counterpart of x is ln(tan(x)+sec(x))
So we can squish any f(x) function by taking f(ln(tanx+secx))
are you aware of the complex identity relating sin, cos, cosh, and sinh?
I'd say I have a surface level understanding
cosh(x) = cos(ix)
sinh(x) = -isin(ix)
maybe something to dig in that direction? Not too sure
i need to reread what you said
Well with the complex identity the hyperbolic counterpart of sin is sinh
But from this perspective sin's counterpart is tanh
Darpleon is relating trig and hyperbolic functions
yeah ik
just rereading to try and see if a hint might come to mind as to where to look for this relation
Oh ok
Well I assume if you just do the algebra with the exponential forms it'll all check out
But that might not provide any additional insight
hmm interesting, for the sinh-tan example, computing sinh(ln(tanx + secx)) does give you something similar to the tan function, but it's missing every second period
same with sech - cos, graph disappears for pi/2 + 2pi * k < x < 3pi/2 + 2pi * k
right okay of course it would, those are intervals where tanx + secx is negative
yes you have to use absolute value
And with cos and sec you're not gonna get negative values
i think i may have maybe some sort of path that could be worth looking at
consider the cos to sech example
cos denotes x coordinates of a circle
while cosh denotes x coords of a hyperbola
considering that a hyperbola is in some sense a sort of inverted circle, i guess it makes sense that 1/cosh and cos should be related?
super loose but maybe worth digging into
technically sec and tan also describe a hyperbola
Due to them having that same identity
yeah
area of a circle is pi r^2
so for circle A, you have 225pi = pi (r_a)^2
do the same for circle B
$sq(x)=\ln(\tan{x}+\sec{x}) \ e^{sq}=\tan{x}+\sec{x} \ e^{-sq}=\frac{1}{\tan{x}+\sec{x}} \ = \frac{\sec{x}-\tan{x}}{\sec^2{x}-\tan^2{x}} \ e^{-sq}=\sec{x}-\tan{x}$
Darpleon
$e^{sq}+e^{-sq}=2\sec{x} \ e^{sq}-e^{-sq}=2\tan{x}$
Darpleon
$\cosh{sq}=\sec{x} \ \sinh{sq}=\tan{x} \ \tanh{sq} =\sin{x}$
Darpleon


