Question

sine/cosine of complementary angles 2 which best describes the relationship between sin α and cos β? a sin α = cos β b sin α ≠ cos β c sin α ≈ cos β d cannot be determined what angle measurement will make the value of sine and cosine equal? a 30° b 45°

Explanation:

Step1: Recall the relationship between sine and cosine of complementary angles

In a right - triangle, \(\alpha+\beta = 90^{\circ}\), so \(\beta=90^{\circ}-\alpha\).
We know the co - function identity: \(\sin\theta=\cos(90^{\circ}-\theta)\) and \(\cos\theta=\sin(90^{\circ}-\theta)\).
Since \(\beta = 90^{\circ}-\alpha\), then \(\cos\beta=\cos(90^{\circ}-\alpha)\)

Step2: Apply the co - function identity

By the co - function identity \(\cos(90^{\circ}-\alpha)=\sin\alpha\)

Answer:

C. \(\sin\alpha=\cos\beta\)