Use the unit​ circle, along with the definitions of the circular​ functions, to find the exact value for the function at the​ right, given s = 7π/6.

Question

.
.

Answer 1

To find the exact value for the function, we need to determine the values of the circular functions at the angle s = 7π/6 radians on the unit circle.

First, let's find the point on the unit circle that corresponds to the angle 7π/6 radians.

In the unit circle, the angle 7π/6 radians is in the third quadrant (Q3).

We know that the point on the unit circle in Q3 has coordinates (x, y) where x < 0 and y < 0.

Since the unit circle has a radius of 1, the coordinates of the point can be found using the following trigonometric identity:

x = cos(s)
y = sin(s)

cos(7π/6) = cos(π/6) = √3/2
sin(7π/6) = sin(π/6) = -1/2

Therefore, the exact value of the function at s = 7π/6 is:
cos(7π/6) = √3/2
sin(7π/6) = -1/2