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View Full Version : Find exact value of composite trig function.


veganazi
Oct5-11, 01:13 PM
1. The problem statement, all variables and given/known data
cos^-1(sin(5pi/4))


2. Relevant equations
n/a


3. 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
Oct5-11, 01:28 PM
sin(5pi/4) = - 1/√2.

ehild

symbolipoint
Oct5-11, 03:08 PM
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.