how to evaluate cos13pi/6 and sin37pi/4?

We'll calculate cos
13pi/6.

We notice that we can
write:

13pi/6 = pi/6 +
12pi/6

pi/6 + 12pi/6 = pi/6 +
2pi

We can substitute 2pi by 0, because 2pi and 0 are
overlapping.

So,

cos 13pi/6
= cos (2pi + pi/6)

cos (2pi + pi/6) = cos 
pi/6

cos 13pi/6 = cos  pi/6 =
sqrt3/2

We'll calculate sin
37pi/4.

We notice that we can
write:

37pi/4 = pi/4 +
36pi/4

pi/4 + 36pi/4 = pi/4 +
9pi

But 9pi = 4*2pi + pi

We'll
substitute 2pi by 0.

4*2pi = 4*0 =
0

cos 37pi/4 = cos (pi/4 +
pi)

cos (pi/4 + pi) = - cos
pi/4

cos 37pi/4 = - cos pi/4 = -
sqrt2/2