Question

Question 5 what general conclusion can you draw about the sines and cosines of complementary angles? state your conclusion in words and in the form of equations.

Answer 1

The sines and cosines of complementary angles (angles that add up to 90°) are equal; sin(α) = cos(90° - α) and cos(α) = sin(90° - α).

Step-by-step explanation:

The general conclusion that you can draw about the sines and cosines of complementary angles is based on the complementary angle theorem in trigonometry. For two angles α (alpha) and β (beta) that are complementary, meaning their measures add up to 90° or π/2 radians, the sine of one angle is equal to the cosine of the other. This relationship is expressed through the equations:

• sin(α) = cos(90° - α)
• cos(α) = sin(90° - α)

These equations show that the sine of angle α is equal to the cosine of its complementary angle (90° - α) and vice versa. Similarly, if angles A and B are complementary, then sin(A) = cos(B) and cos(A) = sin(B).

Using right triangles, where the angles add up to 90°, we can see this property in action. For example, consider a right triangle with angle α and its complementary angle β. If one angle is 30°, the other angle is 60°, and you can observe that sin(30°) is indeed equal to cos(60°).