Question

Find the exact value of the trigonometric function at the given real number?
- Sin (21pi/2)
- Cos (21pi/2)
- Cot (21pi/2)

Answer 1

Okay, for sin(21pi/2) you want to look at what's happening to the angle as it's going around the unit circle. This one's going around 10.5 * pi times, so it's going completely around the circle 5 times, and pi/2 once. So, what is the sin(pi/2)? 1.

Answer 2

Same thing for cos(21pi/2) -- the angle is actually ending up to be pi/2, so what is the cos(pi/2)? 0.

Answer 3

For cot(21pi/2) = cot(pi/2), we look at how cot(x) = cos(x)/sin(x). If cos(pi/2) = 0 and sin(pi/2)=1, then cot(pi/2) = 0/1 = 0.