Trigonometry

[merry heron]

Can someone help with the example 2 question pls

[short hare]

Are you allowed to use a calculator?

[merry heron]

ya

[short hare]

Ok, lets tsart with A

Generally, mathematicians hate denominators

How do you think you can remove x form the denominator?

[merry heron]

do i bring it to tan

[short hare]

And from here, it becomes easy to isolate x. are you able to do it yourself?

[merry heron]

ya. i gotta divide it right?

[short hare]

And what do you get

[merry heron]

7.70

[short hare]

Now do you now how to use inverse trigonometry to solve example B?

[merry heron]

i have no clue on how to do it

[short hare]

$$\cos(\theta) = 0.729$$
$$\cos^{-1}(\cos(\theta)) = \cos^{-1}(0.729)$$

[uneven latch]

@short hare

[merry heron]

all i have to do is make cos negative then i get my answer?

[short hare]

Not negative. This is an inverse function, which is completely different

It essentially undoes the cos function, so it's easy to isolate theta

For now, assume $\cos^{-1}(\cos(\theta)) = \theta$ \
Note: you will find this isn't \textit{always} true in higher level math courses

[uneven latch]

@short hare

[merry heron]

okay. so is the answer 43.19?

[merry heron]

I was able to solve question c too

[short hare]

Nice, what did you get?

Sry for the long delay

[merry heron]

its ok. i got 12

[short hare]

!done

[wispy pike]

If you are done with this channel, please mark your problem as solved by typing .close

[merry heron]

Is it fine if u help with this too pls

Just a)

I’ll brb

[worldly walrus]

I like you wrote things you needed
And since the numbers you need at the ones touching theta you also wrote out adj/hyp
How would you set up the equation to solve for theta?

[merry heron]

Would that be the equation

[worldly walrus]

Thats right!
Okay now do the same thing as the previous problem you got help with to finish the problem
You need to undo the cosine function by using its....(fill in the blank)

[merry heron]

do i need to use inverse function?

[worldly walrus]

Also right!

[merry heron]

so is the answer 6.51 then?

[worldly walrus]

Unless i typed it in my calculator incorrectly. Thats too small. Are you in degrees? Or did you use an incorrect inverse? 😅

[merry heron]

I prob did smth wrong. This is what I put on my calculator

[worldly walrus]

Ah
I found the problem
You typed the wrong numbers 😅
Try again 🤞

[merry heron]

oh shoot

okay so its 14.59

[worldly walrus]

Much better!

[merry heron]

i got one more question. how do ik when to use inverse function?

[worldly walrus]

When your variable is inside a trig function

Like stated above it's the opposite of sine, cosine, and tangent
Think of it like addition and subtraction or multiplication and division

My teach had also stated that trig functions take an angle to spit out a ratio
So the inverse will take a ratio to spit out an angle
I hope that helps

[merry heron]

okay tysm

[worldly walrus]

Of course!
Happy to help

[merry heron]

can someone help me w this plsssssssss

[round remnant]

what is p

q and r

[merry heron]

wdym

like the degree and length for them

[round remnant]

no like

what length is p

[merry heron]

12cm

[round remnant]

in this diagram

what exactly is p

as in length

[merry heron]

i have no clue

0?

[round remnant]

bro 😭🙏

did they give u a diagram

[merry heron]

no i didnt get a diagram

[round remnant]

so

how do i know which one the hypotenuse is

[merry heron]

the longest side right

or do we just guess

[round remnant]

which one is the longest side vro 💔🥀

[merry heron]

oh the hyp

[round remnant]

no shit

like

which length is the hupotenuse

they gave 2 in the question

[merry heron]

ohhh

90

[round remnant]

idk the third one

[merry heron]

did i get it right

[round remnant]

90 is the angle vro

[merry heron]

16.5cm

[round remnant]

the thing is

[round remnant]

is a possibility

but cant be sure

[merry heron]

so how do we know then

[round remnant]

assuming incan take whatever side as whichever one i wish to

this is one case

this is the other case

[merry heron]

okay

[round remnant]

which one do we take

[merry heron]

first one

[round remnant]

ight

so ill assume that the hypotenuse ism16.5

we have to find r

do you know the value of sin53?

degrees

[merry heron]

i dont think so

[round remnant]

wait a min

ill draw u a triangle

easy to remember

[merry heron]

okay

[round remnant]

now can you tell me the value of sin53?

@merry heron

[merry heron]

is it like

0.80

[round remnant]

yeah but just tell it in fractions

easier to remember

now

[merry heron]

but idk how to convert it into fractions on my calculator

[round remnant]

then how did u get 0.8

[round remnant]

use this diagram

not the calculator

its more useful in physics

[merry heron]

but its hard doing it without it

[round remnant]

do you know

what the sine function is?

[merry heron]

ya

[round remnant]

what is it

[merry heron]

its like that button on the calculator

that says sin

[round remnant]

😭

i mean in mathematics

[merry heron]

oh then not rlly

[round remnant]

so basically

in a right angled triangle

the sin of an angle

is the ratio of the opposite side to the hypotenuse with respect to the angke

lemme show a diagram to explain it in simpler words

[merry heron]

thanks

[round remnant]

@merry heron

[merry heron]

for me i use like the opposite and adjacent words

[round remnant]

u can use that too

whatever is easier

[round remnant]

now can you tell me the value of sin53

[worldly walrus]

You can use Soh Cah Toa as a mnemonic as it refers to opposite and adjacent

My class was squirrely so we used Cho Sha Cao for the inverses

[merry heron]

is it like

0.8

[round remnant]

yes but

[merry heron]

thank you

[round remnant]

tell me from the diagram

not from your calculator

[merry heron]

4/5

[round remnant]

nice

now

do you understand how i got this

sorry i forgot to mark the angle

[merry heron]

ya kinda

[round remnant]

but its thr angle between the base and hypotenuse

[round remnant]

how

[merry heron]

from the answer i gave

[round remnant]

yes but

how is it equal to x/16.5

[merry heron]

no clue

is it bc theyre on the same triangle

[round remnant]

hmm

no its the ratio

but wait a min

[worldly walrus]

Took me a min. But i dont think those triangles are similar?

[round remnant]

yo wanna know smth?

[round remnant]

ratio is

sin53 is always constant

either way the diagram is wrong i js realized

[merry heron]

oh okay

[round remnant]

its supposed to look like this

[worldly walrus]

True
But if you were using the 3-4-5 triangle and the one to the problem at hand thats what i meant lol
But i could still be reading the wrong triangles 😅

[round remnant]

no the triangle is similar

just not the same

[merry heron]

should i just give up for that question

[round remnant]

see the problem with the question is

they didnt mentioned what the hypotenuse is

they were supposed togive a diagram atleast

[round remnant]

the logic behind this is that

angle is greater than 45

so height is greater than base

either way

@merry heron

the value of cos53 is 3/5

u need cos53 not sin

[merry heron]

okay thanks

do u think u can help me w one more question plssss?

[round remnant]

ok sure

[round remnant]

also imthink this is the correct case

[round remnant]

the other one is wrong

do u have annanswer kwy?

answer key*

[merry heron]

yeah but it doesnt show for that question for some reason

[round remnant]

it shows for this right

[worldly walrus]

This is fun. I suggest looking at what similarity you can use then find the pieces for it
Like sss, asa, aas, aaa

[merry heron]

not that one

[round remnant]

oh

well

i got the answer

[round remnant]

so these are similar

@merry heron

can you tell me how these are similar?

[merry heron]

ya

abc=edc

[round remnant]

and?

u cant prove similarity using only one angle

you need another pair

[merry heron]

ab=ed bc=dc ac=ec

[round remnant]

no

[worldly walrus]

Not enougb info for sss similarity

[round remnant]

acb=ecd

[round remnant]

you cant prove sss here

[worldly walrus]

Exactly
Not enough for that
So gotta use the other ones

[merry heron]

why is it this one instead

[round remnant]

if two angles are vertically oppoiste

theyre equal

so now u got 2 sets

of angles

which means theyre similar triangles

now do you know what to do?

[merry heron]

no

[round remnant]

so in two similar triangles

the ratios of corresponding sodes are equal

[merry heron]

okay

[round remnant]

now

do you understand what that means

[merry heron]

the sides r the same

[round remnant]

no

the ratios of the sides are thr same

im actuwlly kinda sleepy so im gonna go to bed

but heres the method

[merry heron]

okay thanks. have a good sleep

[merry heron]

does anyone know where the "11"and "x+10" came from ?

nvm

[merry heron]

can someone help me w this question plsplspls. its on my test tmrw plssssssssssssssssssssssssssssssssssss i dont wanna fail it

[worldly walrus]

Looks like the answer is already there
Are you having a hard time understanding why those steps?

[merry heron]

ya i dont get the steps

[worldly walrus]

Okay
So you want to find <Q in the triangle RSQ, but you only have 6cm at the base
You have more information on triangle RSP, and angle and the base of 12cm
So you basically need something they both share to have enough information for triangle RSQ
you with me so far?

[merry heron]

ya

[worldly walrus]

Since they both share segment RS, we need to find its length
We have to use triangle RSP as it has a an angle and a side length. We can use that to figure out RS
From here, do you understand how to decide which trig function to use and how to solve it?

[merry heron]

no i dont rlly know what trig function to use

[worldly walrus]

Thats good to know
Do you understand how to use a trig function?
Like if i gave you a triangle and asked you to find sin(x) would you be able to give me the ratio?

[merry heron]

ya ik how to use it and i can find the ratios too

[worldly walrus]

Perfect!
So take a look at triangle RSP
We got the angle 40, we have PS, and we need RS
which of the trig functions uses those segments in relation to the angle? (as in which pair of sides do you have? Adjacent, opposite, hypotenuse)

[merry heron]

is it adj and opp?

[worldly walrus]

That's right! and which of the 3 trigs uses adj and opp?

[merry heron]

tan

[short hare]

Now can you setup your trigonometric equation?tan(_) = _/_

[merry heron]

tan(40)= 12/opp

or would i replace opp w a variable?

[short hare]

Remember, based on TOA, it should be opp/adj

[merry heron]

oh ya i forgot

tan(40)=opp/12

[worldly walrus]

good good. you can use a variable instead. visually it will look better

[merry heron]

okay ill use x

[worldly walrus]

from there, do you understand how to solve that?

[merry heron]

ya i do. thanksssss

[worldly walrus]

of course!

and do you understand how to solve for angle? you only need to set up another equation using triangle RSQ to finish the problem

[merry heron]

i would use inverse function right

[worldly walrus]

thats right! and can you see which inverse to use?

[merry heron]

the tan inverse?

[worldly walrus]

Now can you setup your trigonometric equation?arctan(_) = _

[merry heron]

idk tbh

i think the way i was gonna do it was gona be wrong

[worldly walrus]

show me anyway

better to know for sure if it is correct or incorrect
then that way you can get corrections if needed

[merry heron]

oh i alr erased it. its bc i forgot to divide 10.1 by 6 thats why

Here’s the new thing that I did tho

[worldly walrus]

nice
did that better help you understand how to solve this type of problem now?

[merry heron]

ya it did. thanks