i have an exam in 9 hours and this particular question is coming up so id apreciate if anyone helps me out with this
#Trigonometry
stone schooner
sudden pendantBOT
i have an exam in 9 hours and this particular question is coming up so id apreci...
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safe spindle
i have an exam in 9 hours and this particular question is coming up so id apreci...
$\tan \left(\frac{A}{2}+\frac{A}{2} \right)=\tan(A)$
oblique ploverBOT
Civil Service Pigeon
stone schooner
$\tan \left(\frac{A}{2}+\frac{A}{2} \right)=\tan(A)$
can u explain further
safe spindle
can u explain further
Expand the LHS and set it equal to 9/40
solemn cobalt
But it says to use the tan(A+B) formula to solve this
safe spindle
That's how you expand the LHS
solemn cobalt
👍
stone schooner
Expand the LHS and set it equal to 9/40
could u please do it on paper
i been trying for hours
and i couldnt
stone schooner
But it says to use the tan(A+B) formula to solve this
do you know how to do that by any chance
?
safe spindle
and i couldnt
Send what you have
stone schooner
Send what you have
i scrapped all the papers
cuz im getting a panic attack
its currently 2 am and my exam is at 10
id apreciate it if u help me do this
safe spindle
b/c you should have the LHS is $$\frac{2\tan(A/2)}{1-\tan^2(A/2)}$$
oblique ploverBOT
Civil Service Pigeon
safe spindle
Mhm
solemn cobalt
@stone schooner do you know about trignometric ratios
stone schooner
it makes perfect sense up to this point
yeah
i did this
is this correct
this is my formula logbook
provided by my school
safe spindle
tan(A)=9/40, not A=9/40
safe spindle
**Civil Service Pigeon**
You should be able to rearrange this as a quadratic in tan(A/2) and solve
oblique ploverBOT
Civil Service Pigeon
safe spindle
This implies $80\tan(A/2)=9-9\tan^2(A/2)$
oblique ploverBOT
Civil Service Pigeon
safe spindle
From here, it's a quadratic in tan(A/2)
stone schooner
**Civil Service Pigeon**
and i just solve for a/2
?
but bro
they tell me not to use this formula
u used this one
they want this one
safe spindle
Setting A=B yields the tan(2A) formula
I just skipped the step of combining like terms
safe spindle
and i just solve for a/2
tan(A/2)*
safe spindle
I just skipped the step of combining like terms
If you want to be extra explicit, you can show this step
stone schooner
If you want to be extra explicit, you can show this step
so
a = 4/90
and
b = a/2
safe spindle
What...
rocky fossil
b = -a/2
stone schooner
we gonna fail @rocky fossil
rocky fossil
howd we find that?
using the formula
tan(a+b) = tanA/2
so a +b = a/2
b = a/2 - a
b = -a/2
stone schooner
oh
safe spindle
b = -a/2
You do notice that the A in the given formula and the A in the tan(A)=9/40 aren't the same, right?
solemn cobalt
Here's how to use the formula for tangent of the sum of angles, tan(A+B), to find the value of tan(A/2), given tan(A) = 9/40.
From the formula for tangent of the sum of angles, we have:
tan(A+B) = (tan(A) + tan(B)) / (1 - tan(A)tan(B))
Let's set B = A/2, so that we can use this formula to find tan(A/2). Then:
tan(A+A/2) = (tan(A) + tan(A/2)) / (1 - tan(A)tan(A/2))
We know that tan(A) = 9/40, so we can substitute this in:
tan(3A/2) = (9/40 + tan(A/2)) / (1 - 9/40 * tan(A/2))
We can solve for tan(A/2) by rearranging and simplifying:
(9/40 + tan(A/2)) / (1 - 9/40 * tan(A/2)) = tan(3A/2)
Multiplying both sides by 1 - 9/40 * tan(A/2), we get:
9/40 + tan(A/2) = (1 - 9/40 * tan(A/2)) * tan(3A/2)
Expanding the right side and collecting terms, we get:
9/40 + tan(A/2) = tan(3A/2) - 9/40 * tan(A/2) * tan(3A/2)
Rearranging and factoring out tan(A/2), we get:
tan(A/2) * (9/40 * tan(3A/2) + 1) = tan(3A/2) - 9/40
Solving for tan(A/2), we get:
tan(A/2) = (tan(3A/2) - 9/40) / (9/40 * tan(3A/2) + 1)
We can substitute the value of tan(3A/2) using the formula for tangent of the sum of angles again:
tan(3A/2) = (tan(A) + tan(A/2)) / (1 - tan(A)tan(A/2))
Substituting the value of tan(A) and simplifying, we get:
tan(3A/2) = (9/40 + tan(A/2)) / (1 - 9/40 tan(A/2))
Substituting this into the expression we derived for tan(A/2), we get:
tan(A/2) = ([(9/40 + tan(A/2)) / (1 - 9/40 tan(A/2))] - 9/40) / (9/40 * [(9/40 + tan(A/2)) / (1 - 9/40 tan(A/2))] + 1)
Simplifying, we get:
tan(A/2) = (9/31) * tan(A/2)
Therefore, tan(A/2) = 9/31.
Hence, the value of tan(A/2) is 9/31.
rocky fossil
tbh idk waht to do after combining them
rocky fossil
You do notice that the A in the given formula and the A in the tan(A)=9/40 aren'...
what
stone schooner
Here's how to use the formula for tangent of the sum of angles, tan(A+B), to fin...
i
love
u
didnt even read it yet
but man ily
safe spindle
,w find tan(A/2) if tan(A)=9/40
oblique ploverBOT
safe spindle
,w tan((1/2)(arctan(9/40))
oblique ploverBOT
rocky fossil
wait a sec bro
so after combining
the terms
what do we do
remove the denominator?
safe spindle
the terms
Once you have $\frac{2\tan(A/2)}{1-\tan^2 (A/2)}=\frac{9}{40}$, yes, you can multiply both sides by the denominator to turn the equation into a quadratic
oblique ploverBOT
Civil Service Pigeon
stone schooner
@rocky fossil @solemn cobalt is him
rocky fossil
**Civil Service Pigeon**
after turning it into a quadratic what should i do
solemn cobalt
remove the denominator?
Take a common denominator
rocky fossil
they dont want the value of a
they jus want u to find tanA/2 on one side
on its own
safe spindle
after turning it into a quadratic what should i do
You can solve for tan(A/2) since it's a quadratic in tan(A/2)
And the question explicitly asks for tan(A/2), not A/2, so idk where you got that from
One of the cases is rejected because of the quadrant A lies in (based off the sign of the extraneous solution)
rocky fossil
You can solve for tan(A/2) since it's a quadratic in tan(A/2)
And the question ...
my bad
BETT
thx so much
G
safe spindle
Anything else?
Especially @stone schooner since you're the one who opened the channel
Cause if not I'm going to close this
rocky fossil
Anything else?
if u have the time
stone schooner
if u have the time
ye
rocky fossil
to go fully through the question
stone schooner
@solemn cobalt are ur dms open
rocky fossil
to find tanA/2
so we can make sure
we did
the right shi
that would be great
if not
safe spindle
Sure, lemme know what you get
rocky fossil
Sure, lemme know what you get
bet
solemn cobalt
<@877853511533080636> are ur dms open
Yeh
stone schooner
💀
rocky fossil
$-9\tan^{2}\left(\frac{a}{2}\right)\ +80\tan\left(\frac{a}{2}\right)\ +9=0$
oblique ploverBOT
jimmy
stone schooner
supposedly
stone schooner
how to fucking do this 💀
rocky fossil
and it cant solve it
safe spindle
You should be able to factor it
rocky fossil
how to fucking do this 💀
civil is a genius wait
safe spindle
Are you and jusi friends?
safe spindle
I assume you'll explain it then?
rocky fossil
its our mock
rocky fossil
I assume you'll explain it then?
yup
rocky fossil
thx
rocky fossil
Have great day!