Find a positive angle less than 2pi that is coterminal with the given angle
A. 425 degrees B. 27π/4

Solution:

The coterminal angles are the angles that have the same initial side and the same terminal sides.

We determine the coterminal angle of a given angle by adding or subtracting 360° or 2π to it.

To find the coterminal angles of an angle θ depending upon whether it is in terms of degrees or radians the formula used are:

In degrees: θ ± 360n and in radians: θ ± 2πn

A.  425°

Subtracting 2π = 360° from 425°,

→ 425° - 360° = 65°

Required angle is 65°

B. 27π/4

→ 27π/4 - 2π = 19π/4 - 2π

= 11π/4 - 2π = 3π/4

Find a positive angle less than 2pi that is coterminal with the given angle
A. 425 degrees B. 27π/4

Summary:

Positive angle less than 2pi that is coterminal with the given angle A. 425 degrees is 65° and B. 27π/4 is 3π/4