Question

Which of the following statements accurately compares the values of sin 30° and cos 30°?

a) sin 30° equals cosine 30°
b) sin 30° is equal to negative cosine 30°
c) sin 30° is greater than cosine 30°
d) sin 30° is less than cosine 30°

Answer 1

The sin 30° is less than cos 30° because sin 30° is 1/2 and cos 30° is √3/2 in a 30-60-90 triangle.

Step-by-step explanation:

The question asks us to compare the values of sin 30° and cos 30°.

Using the definitions of sine and cosine for angles in a right triangle, sin 30° is the ratio of the opposite side to the hypotenuse, and cos 30° is the ratio of the adjacent side to the hypotenuse in a 30-60-90 triangle.

For a 30-60-90 triangle, the side lengths have a ratio of 1 (opposite to the 30° angle): √3 (adjacent to the 30° angle): 2 (hypotenuse). Therefore, sin 30° = 1/2, and cos 30° = √3/2. Comparing these values, we see that sin 30° (1/2) is less than cos 30° (√3/2).

The correct answer to the question is: sin 30° is less than cosine 30° (d).