Question

State a trigonometric ratio that is equivalent to each of the following trig ratios:

a) sin 3pi/10
b) cos 6pi/7
c) -sin 13pi/7
d) -cos 8pi/7

I know what the answers are, but I'm not sure how to derive them (eg. why do you add or subtract the ratios from pi or 2pi?)

Answer 1

This is easier to imagine graphically. take the example of the angle pi/2 to keep things simple. The full rotation is 2pi. so pi is half a turn. The sin is 1 and the cos is 0. if you add pi to pi/2, you get 3pi/2, whose cos is also 0 and whose sin is -1. add another pi to it and you get 5pi/2, which just spins you around back to pi/2.