Question

Hello.. Find an angle between 0 and 2pi (in decimal form) that is coterminal with the given angle.

Answer 1

9514 1404 393

Answer:

  a. 1.88495559215 radians

  b. 5.23598775598 radians

  c. 1.57079632679 radians

  d. 4.93678845564 radians

Step-by-step explanation:

You want the coefficient of pi to be between 0 and 2. That is, you want its value modulo 2--the remainder from division by 2.

  a. 13/5 = 2.6; 2.6 mod 2 = 0.6. 0.6π ≈ 1.88495559215 (as you know)

  b. -13/3 = -4 1/3; -4 1/3 mod 2 = 1 2/3*. 5/3π ≈ 5.23598775598

  c. 57/2 = 28.5; 28.5 mod 2 = 0.5. 0.5π ≈ 1.57079632679

  d. 11/7 = 1 4/7. 11/7π ≈ 4.93678845564

All angles are in radians.

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* My calculator gives the value of -4 1/3 mod 2 as -1/3. We want the positive value, so must add 2 to this. The attachment shows Desmos is smarter than my calculator.