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. SHOW YOUR WORK STEP BY STEP.
π/6
To find the exact values of cos(π/6) and sin(π/6), we can use the unit circle.
Step 1: Draw a unit circle (a circle with a radius of 1) and label the x-axis and y-axis.
Step 2: Mark the angle measurement of π/6 on the unit circle. This angle is located in the first quadrant and forms an equilateral triangle with the x-axis and the radius.
Step 3: The x-coordinate of the point on the unit circle corresponding to π/6 is the value of cos(π/6), and the y-coordinate is the value of sin(π/6).
In this case, the x-coordinate of the point is √3/2 and the y-coordinate is 1/2.
So, cos(π/6) = √3/2 and sin(π/6) = 1/2.