Question

How do I do these type of problems

find the exact value. Do not use a calculator

cos 7pi

Answer 1

2&pi is one full rotation around the circle, so you can think of 2&pi as being the same as 0. so 7 pi is the same as going around the circle 3 full times with 1&pi left over, to figure this out exactly you can do the following:

(7/2) = 3 +1/2
the 3 is how many times we went 2&pi around the circle, and what we have left is (1/2)*2&pi or 1&pi

cos(&pi) = -1


To do another example

sin((9/2)&pi)

well (9/2)/2 is the same as (9/2)*(1/2)=(9/4)

we get 2 + 1/4 so we get 2 full rotations plus 1/4 of a full rotation. A full rotation is just 2&pi so:

2&pi*(1/4) = &pi/2

sin(&pi/2) = 1