Problem 6 Suppose that the terminal point x y associated to

Problem 6:

Suppose that the terminal point, (x, y), associated to t lies in the first quadrant. Show that (a) sin(t + pi) = - sin t (b) tan(t + pi) = tan t

Solution

sin(A + B) = sin A cos B + cos A sin B

a) sin(t + pi) = sin t*cos pi + cos t*sin pi = -sin t = RHS

b) tan(A + B) = (tan A + tan B)/(1 tan A tan B)

tan(t + pi) = (tan t + tan pi)/(1 - tan t*tan pi) = tan t = RHS