Question

At what point does the terminal side of the angle 5π6 in standard position intersect the unit circle? responses (-12, 3√2) begin ordered pair negative one half comma fraction numerator square root of 3 end root end numerator over denominator 2 end fraction end ordered pair (3√2, −12) begin ordered pair fraction numerator square root of 3 end root end numerator over denominator 2 end fraction comma negative one half end ordered pair (-3√2, 12)

Answer 1

The angle of 5π/6 radians intersects the unit circle at the point (-sqrt(3)/2, 1/2). This is determined by using the reference angle π/6 and accounting for the fact that the angle lies in the second quadrant, where the x-coordinate is negative and the y-coordinate is positive.

Step-by-step explanation:

The angle of 5π/6 radians in standard position intercepts the unit circle at a point that can be determined by looking at the reference angle and the quadrant the terminal side lies in. The reference angle for 5π/6 is π/6, and since 5π/6 is in the second quadrant, where sine is positive and cosine is negative, the coordinates can be found using the sine and cosine of π/6 but with a negative sign for the x-coordinate due to the quadrant it's in.

Thus, the point of intersection on the unit circle is (-sqrt(3)/2, 1/2).

This can be derived from knowing that the unit circle has all points (x, y) that satisfy the equation x2 + y2 = 1. For π/6, cos(π/6) = sqrt(3)/2 and sin(π/6) = 1/2. Since 5π/6 is in the second quadrant, the x-coordinate would be negative, but the y-coordinate would remain positive.