Julia S. answered • 07/22/21

Math and Science Made Manageable

Similar to your other posted problem, we're limited to radians of 0 to 2π. The equation can be simplified as follows:

25 + 15tanθ = 12tanθ +28

15tanθ = 12tanθ + 3

3tanθ = 3

tanθ = 1

Since we know tanθ = sinθ/cosθ, we're looking for places on our unit circle where sinθ and cosθ are the same value. This occurs at π/4 and 5π/4. I did not include 3π/4 or 7π/4 because although the numerical values are the same, the signs are not, meaning tanθ = -1 in those angles, NOT 1.