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
7π/4
To find the exact values of cos(7π/4) and sin(7π/4), we need to remember the unit circle.
The angle 7π/4 is in the fourth quadrant. The reference angle is π/4 since it is the angle formed between the terminal side of the given angle and the x-axis.
The values on the unit circle for π/4 are:
cos(π/4) = 1/√2
sin(π/4) = 1/√2
Since the angle 7π/4 is in the fourth quadrant, the values of cos(7π/4) and sin(7π/4) are the negatives of the corresponding values for π/4.
cos(7π/4) = -1/√2
sin(7π/4) = -1/√2