Finding the angles of a sine function.

Question

Let again t be the angle between 0 and \frac{\pi}{2} such that
sin t = 1/4
Then
cos (t+pi) = .
sin(t-pi) = .
cos (t+2pi) = .
tan (t+pi) =

Answer 1

Apply the addition and subtraction angle identities for the given value of t.

 

cos(t + pi) = cos(t)cos(pi) - sin(t)sin(pi)

cos(t - pi) = cos(t)cos(pi) + sin(t)sin(pi)

sin(t + pi) = sin(t)cos(pi) + cos(t)sin(pi)

sin(t - pi) = sin(t)cos(pi) - cos(t)sin(pi)

 

tan(t + pi) = [tan(t) + tan(pi)] / [1 + tan(t)tan(pi)]

tan(t - pi) = [tan(t) + tan(pi)] / [1 + tan(t)tan(pi)]

 

 

Since the angle t is between 0 and pi/2, the angle is located in the 1st quadrant.