The measure 0 of an angle in standard position is given. Find the exact values of cos 0 and sin 0 for the angle measure and show your all your work.

π/6

To find the values of cos(𝜃) and sin(𝜃) for an angle measure of 𝜋/6 (pi/6), we can use the unit circle.

In the unit circle, an angle of 𝜋/6 is formed by rotating from the positive x-axis in the counterclockwise direction. This angle intersects the unit circle at the point (cos(𝜋/6), sin(𝜋/6)).

To find the values, we can use the trigonometric ratios for this angle.

cos(𝜋/6) represents the x-coordinate of the point on the unit circle, and sin(𝜋/6) represents the y-coordinate of the point.

From the unit circle, we can see that the x-coordinate of the point (cos(𝜋/6), sin(𝜋/6)) is √3/2, and the y-coordinate is 1/2.

Therefore, cos(𝜋/6) = √3/2 and sin(𝜋/6) = 1/2.