Question

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

a. 13pi/5
b. -13pi/3
c. 57pi/2
d. 11pi/7

I know the answer to the first one is 1.88495559215. However, following the formula I was given by my teacher gives me decimals that are higher than the decimal for 2pi or lower than 0, so the other questions keep being wrong. Can someone please help?? I have no idea what to do.

Answer 1

9514 1404 393

Answer:

a. 1.88495559215 radians

b. 5.23598775598 radians

c. 1.57079632679 radians

d. 4.93678845564 radians

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.