Question

What is the corresponding point on the unit circle for the given radian measure? θ = 7 ⁢ π6 a. ( - 1 2 , - 3 2 ) b. ( - 3 2 , - 1 2 ) c. ( 1 2 , 3 2 ) d. ( 3 2 , 1 2 )

Answer 1

The corresponding point on the unit circle for the given radian measure θ = 7π/6 is (-3/2, -1/2).

Step-by-step explanation:

To determine the corresponding point on the unit circle for the given radian measure θ = 7π/6, we can use the reference angle of π/6 and the properties of the unit circle. Since the radian measure is positive and greater than π/2, the point will be in the third quadrant.

The corresponding point on the unit circle in the third quadrant is (-cos(π/6), -sin(π/6)). Evaluating the trigonometric functions, we get (-√3/2, -1/2).

Therefore, the corresponding point on the unit circle for θ = 7π/6 is (b) (-3/2, -1/2).