Let theta be an angle such that sin(theta) = 4/5 and cos(theta) = 3/5. What are cos(theta - pi) and cos(theta - pi/2), in that order?

Answer 1

To find cos(theta - pi), we can use the identity cos(x - pi) = -cos(x).

Since cos(theta) = 3/5, we have cos(theta - pi) = -cos(theta) = -3/5.

To find cos(theta - pi/2), we can use the identity cos(x - pi/2) = -sin(x).

Since sin(theta) = 4/5, we have cos(theta - pi/2) = -sin(theta) = -(4/5) = -4/5.

Therefore, cos(theta - pi) = -3/5 and cos(theta - pi/2) = -4/5.