Question

help with inverse trig functions?

Answer 1

Find the exact value of sin(arctan(2)). For full credit, explain your reasoning.

Answer 2

well first try to make than tan inverse inside the bracket to sin inverse so that we get sin (sin-1)

Answer 3

drawing a triangle can help you do that

Answer 4

Drawing a triangle will help change tan-1 to sin-1?

Answer 5

Let arctan 2 = x
so, tan x = 2 /1
since you know tan x = opposite side/adjacent side
make a right angled triangle with one leg =2 and other leg = 1

now can you find the hypotenuse ??

Answer 6

yep :) just draw ..you will see

Answer 7

once you find the hypotenuse, find sin x.

Answer 8

sqrt 5

Answer 9

because sin(arctan(2)). = sin x

Answer 10

yes, so sin x = sin (arctan 2) =...?

Answer 11

sqrt5?

Answer 12

thats the hypotenuse .
sin ratio = opposite side / hypotenuse =... ?

Answer 13

oh so it's 2/sqrt5

Answer 14

yup .

Answer 15

any doubts ?

Answer 16

alright and what about finding the exact real value of arccos(sqrt2/2)?

Answer 17

no I understand that now that you have to use a tiangle to solve it

Answer 18

arccos(sqrt2/2) =x
cos x = sqrt2/2 = 1/sqrt 2
for what value of angle 'x' is cos x = 1/sqrt 2
its one of the standard angle....

Answer 19

also, next time please ask new question in new post...

Answer 20

okay sorry. I am not sure how you got cos x = sqrt2/2 = 1/sqrt 2 ?

Answer 21

you know unit circle ?
which defines standard values of sin/cos for standard angles...

Answer 22

i suggest you learn and remember all standard angles and values..

Answer 23

yes i know the unit circle. is that pi/4? 45 degrees?

Answer 24

yes, exactly :)

Answer 25

so pi/4 would be the exact real value?

Answer 26

\[\arccos(\frac{\sqrt{2}}{2})\] see if you recall an angle whose cosine is \(\frac{\sqrt{2}}{2}\)

Answer 27

yes.
pi/4 in radians
45 in degrees.

Answer 28

Thank you so much!

Answer 29

welcome ^_^