SOLUTION: Find the exact value, if possible without a calculator. If it is not possible, explain why. {{{tan^-1(sin(-5pi/2))}}}

Algebra ->  Trigonometry-basics -> SOLUTION: Find the exact value, if possible without a calculator. If it is not possible, explain why. {{{tan^-1(sin(-5pi/2))}}}      Log On


   

Question 1178878: Find the exact value, if possible without a calculator. If it is not possible, explain why.
tan%5E-1%28sin%28-5pi%2F2%29%29
Answer by ikleyn(52919) About Me  (Show Source):
You can put this solution on YOUR website!
.

Geometrically, the angle  -5pi%2F2  is the same as  -pi%2F2.



Therefore,  sin%28-5pi%2F2%29 = sin%28-pi%2F2%29 = -1.


arctan(-1) = -pi%2F4.                     ANSWER


tan%5E%28-1%29%28-1%29 = -pi%2F4+%2B+k%2Api.            ANSWER

Solved, answered and explained.