Question

Algebra 2 and geometry is part of this. On question 11

Answer 1

`coterminal\text{ angle}=(2\pi)/(3)`

Explanations

The coterminal of angle is determined by adding or subtracting 360 degrees (2pi) from the reference angle.

Given the reference angle in radians as shown:

`(14\pi)/(3)`

Subtract 360 degerees (2π) from the angle to have

`\begin{gathered} (14\pi)/(3)-2\pi=(14\pi-6\pi)/(3)=(8\pi)/(3) \\ \end{gathered}`

Subtract 2π from the result to have:

`(8\pi)/(3)-2\pi=(8\pi-6\pi)/(3)=(2\pi)/(3)`

Hence the coterminal angle that lies between 0 and 2π radians is 2π/3 rad