COTERMINAL ANGLES WORKSHEET

Problem 1 :

Find a positive and a negative angle that are coterminal with the angle 75°.

Problem 2 :

Find a positive and a negative angle that are coterminal with the angle 2π/3.

Problem 3 :

Find a positive and a negative angle that are coterminal with the angle -200°.

Problem 4 :

Find a positive and a negative angle that are coterminal with the angle π/8.

Problem 5 :

Find a positive and a negative angle that are coterminal with the angle 410°.

Problem 6 :

Find a positive and a negative angle that are coterminal with the angle 13π/4.

1. Answer :

Positive angle that is coterminal with 75° :

75° + 360° = 435°

So, positive angle that is coterminal with 75° is 435°.

Negative angle that is coterminal with 75° :

75° - 360° = -285°

So, negative angle that is coterminal with 75° is -285°.

2. Answer :

Positive angle that is coterminal with 2π/3 :

2π/3 + 2π = 2π/3 + 6π/3

2π/3 + 2π = (2π + 6π)/3

2π/3 + 2π = 8π/3

So, positive angle that is coterminal with 2π/3 is 8π/3.

Negative angle that is coterminal with 2π/3 :

2π/3 - 2π = 2π/3 - 6π/3

2π/3 - 2π = (2π - 6π)/3

2π/3 - 2π = -4π/3

So, negative angle that is coterminal with 2π/3 is -4π/3.

3. Answer :

Positive angle that is coterminal with -200° :

-200° + 360° = 160°

So, positive angle that is coterminal with -200° is 160°.

Negative angle that is coterminal with -200° :

-200° - 360° = -560°

So, negative angle that is coterminal with -200° is -560°.

4. Answer :

Positive angle that is coterminal with π/8 :

π/8 + 2π = π/8 + 16π/8

π/8 + 2π = (π + 16π)/8

π/8 + 2π = 17π/8

So, positive angle that is coterminal with π/8 is 17π/8.

Negative angle that is coterminal with π/8 :

π/8 - 2π = π/8 - 16π/8

π/8 - 2π = (π - 16π)/8

π/8 - 2π = -15π/8

So, negative angle that is coterminal with π/8 is -15π/8.

5. Answer :

Positive angle that is coterminal with 410° :

Because the given angle 410° is more than 360°, to get the positive angle that is coterminal with 410°, subtract 360° from 410°.

410° - 360° = 50°

So, positive angle that is coterminal with 410° is 50°.

Negative angle that is coterminal with 410° :

Because the given angle 410° is more than 360° and less than 720° (two times of 360°), to get the negative angle that is coterminal with 410°, subtract 720° from 410°.

410° - 720° = -310°

So, negative angle that is coterminal with 410° is -310°.

6. Answer :

Positive angle that is coterminal with 5π/4 :

Because the given angle 13π/4 is more than 2π, to get the positive angle that is coterminal with 13π/4, subtract 2π from 13π/4.

13π/4 - 2π = 13π/4 - 8π/4

13π/4 - 2π = (13π - 8π)/4

13π/4 - 2π = 5π/4

So, positive angle that is coterminal with 13π/4 is 5π/4.

Negative angle that is coterminal with 13π/4 :

Because the given angle 13π/4 is more than 2π and less than 4π (two times of 2π), to get the negative angle that is coterminal with 13π/4, subtract 4π from 13π/4.

13π/4 - 4π = 13π/4 - 16π/4

13π/4 - 4π = (13π - 16π)/4

13π/4 - 4π = -3π/4

So, negative angle that is coterminal with 13π/4 is -3π/4.

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