Use reference angles to find the exact value of the expression cos17π/4. Show all your work
To find the exact value of the expression cos(17π/4), we can use the concept of reference angles and the unit circle.
First, we need to determine the reference angle for the given angle of 17π/4. The reference angle is the acute angle formed between the terminal side of the angle and the x-axis.
To find the reference angle, we can subtract full revolutions (2π) from the given angle until we get an angle between 0 and 2π. In this case, we have:
17π/4 = (16π/4 + 1π/4) = 4π + π/4
Since 4π is equivalent to 0 degrees or 360 degrees, we can focus on the π/4 part.
Now, this reference angle of π/4 corresponding to 45 degrees has special trigonometric values on the unit circle. The reference angle lies in the first quadrant, where cosine is positive.
The cosine function of the reference angle π/4 is √2/2.
Since the angle 17π/4 is in the fourth quadrant (360 degrees - 315 degrees), the sign of the cosine function will be negative.
Therefore, cos(17π/4) = -√2/2.
So, the exact value of the expression cos(17π/4) is -√2/2.