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.
4π/3 radians
To find the exact values of cos (4π/3) and sin (4π/3), we can use the unit circle.
First, let's determine the reference angle. The reference angle is the acute angle formed by the terminal side of the angle and the x-axis.
Since 4π/3 is greater than π, we need to subtract π to get the reference angle:
Reference angle = 4π/3 - π = π/3
Now, let's evaluate the values on the unit circle for the reference angle of π/3:
The cosine of π/3 is the x-coordinate of the point on the unit circle, which is 1/2.
So, cos (4π/3) = 1/2.
The sine of π/3 is the y-coordinate of the point on the unit circle, which is √3/2.
So, sin (4π/3) = √3/2.
Therefore, the exact values of cos (4π/3) and sin (4π/3) are 1/2 and √3/2, respectively.