If you know the radius of the circle and the measure of an angle $\theta$ in standard position, which trigonometric function gives the ratio of the length of the side opposite $\theta$ to the hypotenuse in a right triangle?

• A. $\tan \theta$
• B. $\sin \theta$
• C. $\cot \theta$
• D. $\cos \theta$

Answer: (B)

Verified step by step guidance

1. Recall the definitions of the primary trigonometric functions in a right triangle with an angle \( \theta \):
2. The sine function is defined as the ratio of the length of the side opposite the angle \( \theta \) to the hypotenuse, expressed as \( \sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} \).
3. The cosine function is the ratio of the adjacent side to the hypotenuse: \( \cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}} \).
4. The tangent function is the ratio of the opposite side to the adjacent side: \( \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} \).
5. Since the problem asks for the ratio of the side opposite \( \theta \) to the hypotenuse, the trigonometric function that represents this ratio is \( \sin(\theta) \).