Coterminal angles are angles that have the same initial side and the same terminal sides. We determine coterminal angle of a given angle by adding or subtracting 360° or 2π.
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.
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May 21, 24 08:51 AM
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