Find exact value of composite trig function.

[veganazi]

Homework Statement

cos^-1(sin(5pi/4))

Homework Equations

n/a

The Attempt at a Solution

I began by finding the reference angle of 5pi/4 by subtracting pi, and I got pi/4. pi/4 must be part of an isosceles right triangle, so I drew a diagram with sides 1,1, and √2. I found sin pi/4 to equal 1/√2, which I rationalized and got √2/2. I viewed my cosine chart, and cosine is √2/2 where the angle is pi/4. I answered pi/4 into MyMathLab, which found it incorrect, so I concluded that I am most likely doing it wrong.

 

[ehild]

sin(5pi/4) = - 1/√2.

ehild

 

[symbolipoint]

You might also be able to use the fact that sine and cosine are typically π/2 out of phase, and that cos^-1(cos(x))=x.