Question

TRIGONOMETRY Melinda and Walter were both solving the same trigonometry problem. However, after they finished their computations, Melinda said the answer was 52 sin 27° and Walter said the answer was 52 cos 63º. Could they both be correct?

Answer 1

Both Melinda's and Walter's answers are correct as they are mathematically equivalent due to the co-function identities of sine and cosine, applying the fact that 63° and 27° are complementary angles.

Step-by-step explanation:

When Melinda said the answer was 52 sin 27° and Walter said it was 52 cos 63°, we need to consider the properties of sine and cosine in a right triangle or the unit circle to determine if they could both be correct.

Using the co-function identities, which are sin(90° - θ) = cos(θ) and cos(90° - θ) = sin(θ), we can analyze their answers. Since 63° is the complement of 27° (they add up to 90°), the identities suggest that sin(27°) is equal to cos(63°).

Thus, both answers are mathematically equivalent, meaning that yes, Melinda and Walter could both be correct.