Question

Determine (costheta) when (tantheta = -√3) and (sin(-theta) = -3/√2).

A. (√3/2)

B. (-√3/2)

C. (1/2)

D. (-1/2)

Answer 1

The value of cos(theta) is determined to be √3/2 (option A) by using trigonometric identities and considering the signs of the given trigonometric functions, which indicate that theta is in the fourth quadrant.

Step-by-step explanation:

To determine the value of cos(theta) when tan(theta) = -√3 and sin(-theta) = -3/√2, we can use trigonometric identities and the given information. The negative sign in the tangent indicates that the angle theta is either in the second or fourth quadrant. The sine function is negative in the fourth quadrant, which matches our second condition, so theta is in the fourth quadrant.

In the fourth quadrant, cosine is positive, and because the sine is -3/√2 (which corresponds to a 3-4-5 reference triangle), the cosine must be √3/2. Therefore, cos(theta) = √3/2 which corresponds to answer choice A.