How do you find the reference angles...

Question

How do you find the reference angles of ...

1. 5π/4

2. 5π/6

3. 9π/8

 

Answer 1

1. 5π/4= 4π/4 + π/4 = π+π/4 Hence, the reference angle is π/4 fro the x-axis. Moreover, 5π/4 is in the third quadrant.

 

2. 5π/6 = 3π/6 + 2π/6 =π/2+π/3.Thus, this angle is in the second quadrant. Hence the reference angle can be found by subtracting the given angle 5π/6 from π.

 

Therefore, the reference angle is π-5π/6=6π/6-5π/6=π/6.

 

3 9π/8=π+π/8. Hence the reference angle is π/8.

Answer 2

A reference angle is the smallest angle that the terminal side of a given angle makes with the x-axis.

 

5π/4, π/4

5π/6, π/6

9π/8, π/8

 

Look at these on a unit circle.