Find a positive angle less than 2π that is coterminal with:
465°, 27π/4

Solution:

Two angles are coterminal when the angels themselves are different, but their sides and vertices are identical.

There is an infinite number of coterminal angles of a given angle. Additionally, there the values of the coterminal angles may be negative or positive

1. Given angle = 465°

465° = 31/12 π ≈ 2.583 π

Coterminal angle in [0, 360°) range:

105°, located in the second quadrant.

Positive coterminal angles: 105°, 465°, 825°, 1185°, 1545°...

Negative coterminal angles: -255°, -615°, -975°, -1335°...

2. Given angle = 27π/4

27/4 π = 1215°

Coterminal angle in [0, 2π) range: 3/4 π, located in the second quadrant.

Positive coterminal angles:

11π/4, 19π/4 , 27π/4, 35π/4

Negative coterminal angles:

-5π/4, -13π/4, -21π/4, -29π/4

So, less than 2π is only 3/4 π

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Find a positive angle less than 2π that is coterminal with:
465∘, 27π/4

Summary:

A positive angle less than 2π that is coterminal with: 465° is 105° and 27π/4 is 3/4π.