REFERENCE ANGLES WORKSHEET

Find the reference angles for the following angle measures.

1)  5π/3

2)  240°

3)  870°

4)  8π/3

5)  -135°

6)  -13π/4

1. Answer :

The given angle 5π/3 (or 150°) is less than 2π (or 360°). 

The reference angle is the acute angle formed by the terminal side of the angle 5π/3 and the x-axis (see the figure shown below).

The angle 5π/3 has its terminal side in quadrant IV, as shown below.

So, the reference angle is

=  2π - 5π/3

=  π/3

2. Answer :

The given angle 240° is less than 360°. 

The angle 240° has its terminal side in quadrant III, as shown below.

So, the reference angle is

= 240° - 180°

= 60°

3. Answer :

The given angle 870° is greater than 360°.

Find the positive angle between 0° and 360° that is coterminal with 870°.

Divide 870° by 360° and take the remainder.

870° ÷ 360° ---> Remainder = 150°

The positive angle between 0° and 360° that is coterminal with 870° is 150°.

The angle 150° has its terminal side in quadrant III, as shown below.

So the reference angle is

= 180° - 150°

= 30°

4. Answer :

The given angle 8π/3 is greater than 2π.

Find the positive angle between 0 and 2π that is coterminal with 8π/3.

To make the process easier, convert 8π/3 radians to degrees.

8π/3 = 8(180°)/3 = 480°

Divide 480° by 360° and take the remainder.

480° ÷ 360° ---> Remainder = 120°

The terminal side of the angle 120° is in quadrant II.

120° ⋅ π/180° = 2π/3 radians

So, the reference angle is

= π - 2π/3

= π/3

5. Answer :

The given angle -135° is negative.

Add multiples of 360° to -135° to make the angle as positive such that it is between 0° and 360°.

-135° + 360° = 225°

225° is positive and less than 360°.

The terminal side of the angle 225° is in quadrant III.

So, the reference angle is

= 225° - 180°

= 45°

6. Answer :

The given angle -13π/4 is negative.

Add multiples of 2π to -13π/4 to make the angle as positive such that it is between 0 and 2π.

-13π/4 + 2(2π) = -13π/4 + 4π = 3π/4

3π/4 is positive and less than 2π.

The terminal side of the angle 3π/4 (or 135°) is in quadrant II.

So, the reference angle is

= π - 3π/4

= π/4

Kindly mail your feedback to v4formath@gmail.com

We always appreciate your feedback.