FIND A COTERMINAL ANGLE BETWEEN 0 AND 2PIE

Find a coterminal angle between 0 and 2π for each given angle.

Problem 1 :

Solution :

Positive angle that is coterminal with 5π/2 :

So, positive angle that is coterminal with 5π/2 is 9π/2.

Negative angle that is coterminal with 5π/2 :

So, negative angle that is coterminal with 5π/2 is π/2.

Problem 2 :

Solution :

Positive angle that is coterminal with 71π/12 :

So, positive angle that is coterminal with 71π/12 is 95π/12.

Negative angle that is coterminal with 71π/12 :

So, negative angle that is coterminal with 71π/12 is 47π/12.

Problem 3 :

Solution :

Positive angle that is coterminal with 23π/6 :

So, negative angle that is coterminal with 23π/6 is 35π/6.

Negative angle that is coterminal with 23π/6 :

So, negative angle that is coterminal with 23π/6 is 11π/6.

Problem 4 :

Solution :

Positive angle that is coterminal with -17π/36 :

So, positive angle that is coterminal with -17π/36 is 55π/36.

Negative angle that is coterminal with -17π/36 :

So, negative angle that is coterminal with -17π/36 is -89π/36.

Problem 5 :

Solution :

Positive angle that is coterminal with 65π/12 :

So, positive angle that is coterminal with 65π/12 is 89π/12.

Negative angle that is coterminal with 65π/12 :

So, negative angle that is coterminal with 65π/12 is 41π/12.

Problem 6 :

Solution :

Positive angle that is coterminal with 124π/45 :

So, positive angle that is coterminal with 124π/45 is 214π/45.

Negative angle that is coterminal with 124π/45 :

So, negative angle that is coterminal with 124π/45 is 34π/45.

Problem 7 :

Solution :

Positive angle that is coterminal with -23π/12 :

So, positive angle that is coterminal with -23π/12 is π/12.

Negative angle that is coterminal with -23π/12 :

So, negative angle that is coterminal with -23π/12 is -47π/12.

Problem 8 :

Solution :

Positive angle that is coterminal with 31π/12 :

So, positive angle that is coterminal with 31π/12 is 55π/12.

Negative angle that is coterminal with 31π/12 :

So, negative angle that is coterminal with 31π/12 is 7π/12.

Problem 9 :

Solution :

Positive angle that is coterminal with -7π/12 :

So, positive angle that is coterminal with -7π/12 is 17π/12.

Negative angle that is coterminal with -7π/12 :

So, negative angle that is coterminal with -7π/12 is -31π/12.

Problem 10 :

Solution :

Positive angle that is coterminal with 35π/12 :

So, positive angle that is coterminal with 35π/12 is 69π/12.

Negative angle that is coterminal with 35π/12 :

So, negative angle that is coterminal with 35π/12 is 11π/12.

Problem 11 :

Solution :

Positive angle that is coterminal with -5π/4 :

So, positive angle that is coterminal with -5π/4 is 3π/4.

Negative angle that is coterminal with -5π/4 :

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

Problem 12 :

Solution :

Positive angle that is coterminal with 22π/9 :

So, positive angle that is coterminal with 22π/9 is 40π/9.

Negative angle that is coterminal with 22π/9 :

So, negative angle that is coterminal with 22π/9 is 4π/9.

Problem 13 :

-π

Solution :

Positive angle that is coterminal with -π :

-π + 2π = π

So, positive angle that is coterminal with -π is π.

Negative angle that is coterminal with -π :

-π - 2π = -3π

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

Problem 14 :

Solution :

Positive angle that is coterminal with  11π/3 :

So, positive angle that is coterminal with 11π/3 is 17π/3.

Negative angle that is coterminal with 11π/3 :

So, negative angle that is coterminal with 11π/3 is 5π/3.

Problem 15 :

Solution :

Positive angle that is coterminal with  -19π/45 :

So, positive angle that is coterminal with -19π/45 is 71π/45.

Negative angle that is coterminal with -19π/45 :

So, negative angle that is coterminal with -19π/45 is -109π/45.

Problem 16 :

Solution :

Positive angle that is coterminal with  11π/4 :

So, positive angle that is coterminal with 11π/4 is 19π/4.

Negative angle that is coterminal with 11π/4 :

So, negative angle that is coterminal with 11π/4 is 3π/4.