Question

How to solve for Arcsin(cos 5pi/8)???

Answer 1

\[\sin^{-1}(\cos(\frac{5 \pi}{8}))\]

Answer 2

You need to convert the inner cos into sin, and you are done.. :)

Answer 3

\[
\cos(x) = \sin(\frac \pi 2 - x)
\]

Answer 4

Yeah we can do this also.. :)

Answer 5

arcsin=-5pi

Answer 6

cos=5pi/8
usetriangle a2+b2=c2
solver for opp
arcsin=opp/adj
simplify to get arcsin=-5pi

Answer 7

\[
\sin^{-1}(\cos(\frac{5 \pi}{8})) = \sin^{-1}(\sin(\frac \pi 2 - \frac{5 \pi}{8})) =
\sin^{-1}(\sin(\frac 4\pi 8 - \frac{5 \pi}{8})) = \\
\sin^{-1}(\sin(-\frac {\pi}{8})) = -\frac{\pi}{8}
\]

Answer 8

If you do the other way pi/2=5pi/8=pi/8, so you get two answers

Answer 9

negative because arc -pi/8

Answer 10

http://www.wolframalpha.com/input/?i=arcsin%28cos+%285+*pi%2F8%29%29

Answer 11

so two solutions depend on the formula you use, so -5pi, or -pi/8

Answer 12

I just checked and -pi/8 was also the final answer in the problem set that I'm answering but thanks to everyone for your efforts

Answer 13

it just depends what formula you use, you will get different answers

Answer 14

@aum I have a question why did you subtract 5pi/8 from pi/2? is it because of the range of arcsin?

Answer 15

-5pi is not the correct answer.

sin(-5pi) is not equal to cos(5pi/8)

Answer 16

because cos(x) can be written as sin(pi/2 - x)

Answer 17

formula sin(pi/2-5pi/8) use your fx and solver

Answer 18

what I did was use a right triangle
we know cos adj/opp
so solve for opp =8-5pi/8

Answer 19

Noticed a typo in an earlier reply:
\[
\sin^{-1}(\cos(\frac{5 \pi}{8})) = \sin^{-1}(\sin(\frac \pi 2 - \frac{5 \pi}{8})) =
\sin^{-1}(\sin(\frac {4\pi}{ 8} - \frac{5 \pi}{8})) = \\
\sin^{-1}(\sin(-\frac {\pi}{8})) = -\frac{\pi}{8}
\]

Answer 20

sin opp/hyp 8-5pi/8 simplify get 5pi

Answer 21

aum is using the trig identites, so what ever way is easier for you, do it

Answer 22

he is using the cofunction identites

Answer 23

5pi/8 is an ANGLE. It is not the sides. So the adjacent is not 5pi and the hypotenuse is not 8. 5pi/8 = 112.5 degrees.

Answer 24

Yeah you are right, if you had sides then you could have done it that way