How do I do these type of problems
find the exact value. Do not use a calculator
cos 7pi
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