Use reference angles to find the exact value of the expression cos 21π/4. Show all your work.
To find the exact value of cos (21π/4), first we need to find the reference angle for (21π/4).
Since one full revolution around the unit circle is equal to 2π radians, we can subtract 2π from the given angle to bring it within one revolution.
21π/4 - 2π = 21π/4 - 8π/4 = 13π/4.
The reference angle for (21π/4) is 13π/4.
Next, we need to determine the cosine value for this reference angle. The reference angle of 13π/4 is measured counterclockwise from the positive x-axis to the terminal side of the angle.
Looking at the unit circle, we see that at this reference angle, the x-coordinate is 0 and the y-coordinate is -1.
Therefore, cos (13π/4) = 0/1 = 0.
Hence, the exact value of cos (21π/4) is 0.