Question

Use complete sentences to explain the relationship between tan 5pi/4 and tan pi/4. In your answer, reference specific values on the unit circle to prove the relationship between the angles.

Answer 1

Remark
pi/4 is between 0 and pi/2 which means that pi/4 is in the first quadrant.

5*pi / 4 is between pi and 3/2 pi which means that the angle is in the third quadrant. 

So you are talking about one two angles that are in the first and third quadrants.

Step One
Find the Tangent of pi/4 using the unit circle as a reference.

Since pi/4 is 1/2 way between 0 and pi/2 you are referring to something that has and x value of 0.707 for an x value and 0.707 for a y value. (They are equal)

That is the point where the opposite / adjacent = 0.707/0.707 = 1

Step Two
Find the tangent of 5pi/4 using the unit circle.
Using the same argument as pi/4 this time the opposite / adjacent = -0.707/-0.707 = 1 ( the two minus signs cancel out.)