Question

If cos(75°) = sin() and 0° < < 90°, then = _______degrees

Answer 1

Using the complementary angle identity and the one-to-one property of cosine, we find that if cos(75°) = sin(θ) for 0° < θ < 90°, then θ must be equal to 15°.

Step-by-step explanation:

To find the value of θ when cos(75°) = sin(θ) and 0° < θ < 90°, we use the complementary angle identity, which states that sin(θ) = cos(90° - θ). Therefore, cos(75°) = cos(90° - θ). Since cos is a one-to-one function in the range 0° to 90°, the only way for these two cosines to be equal is if their angles are the same. This gives us 75° = 90° - θ, which leads to θ = 15°.