Question

what angle measurement will make the value of sine and cosine equal? a 30° b 45° c 60° d 90°

Explanation:

Step1: Recall trigonometric identities

In a right - triangle, \(\sin\alpha=\frac{\text{opposite}}{\text{hypotenuse}}\) and \(\cos\alpha=\frac{\text{adjacent}}{\text{hypotenuse}}\). We want to find \(\alpha\) such that \(\sin\alpha = \cos\alpha\).

Step2: Use the relationship between sine and cosine

We know that \(\sin\alpha=\cos(90^{\circ}-\alpha)\). If \(\sin\alpha=\cos\alpha\), then \(\alpha = 90^{\circ}-\alpha\).

Step3: Solve the equation for \(\alpha\)

Add \(\alpha\) to both sides of the equation \( \alpha = 90^{\circ}-\alpha\). We get \(2\alpha=90^{\circ}\). Then divide both sides by 2: \(\alpha = 45^{\circ}\).

Answer:

B. \(45^{\circ}\)