Final answer:
The values of theta that make each statement true are 30 degrees, any value of theta, 70 degrees, and 30 degrees.
Step-by-step explanation:
To find the values of theta that make each statement true, we can solve each equation individually.
(a) cos 60 = sin theta
Since cos 60 = 1/2, we have: 1/2 = sin theta. Solving for theta, we find theta = 30 degrees.
(b) cos theta = sin(theta - 30) = cos theta
This equation is true for any value of theta, as cos theta is equal to itself.
(c) sin theta = cos(theta + 20)
Solving for theta, we find theta = 70 degrees.
(d) sin(theta - 60) = cos theta
This equation is true for theta = 30 degrees.
Therefore, the values of theta that make each statement true are: (a) 30 degrees, (b) any value of theta, (c) 70 degrees, (d) 30 degrees.