Angle Measures 6.1 (13)

Question

Find an angle between 0 and 2𝜋 that is coterminal with the given angle.

23𝜋

Answer 1

Just divide by 2𝜋. The remainder will be the coterminal angle in radians.

Answer 2

23pi is coterminal with 23pi+2pin where n = any integer

such as 23pi-24pi = -pi, 23pi+24pi = pi

Answer 3

To find coterminal angles, add or subtract the angle by full revolutions–by a multiple of 2𝜋 (or 360º). The formula is as follows,

x + 2𝜋k

where x is the angle in radians and k is the amount of full revolutions required to find a coterminal angle within the given range (0 to 2𝜋). If the angle value is smaller than the range the k-value will be positive, and if the angle value is larger than the range the k-value will be negative.

To find k here, divide the x value by 2𝜋 and take the whole number. If the angle value were 9𝜋,

9𝜋 ÷ 2𝜋 = 4.5 so,

k = 4

But the angle value is larger than the range so,

k = -4

From there plug the values into the formula, and it will give you a coterminal angle within 0 and 2𝜋.