Question

Find one positive AND one negative angle that are co-terminal with the given angle.(5)/4 Be sure to label and leave your answers in radians (not degrees).

Answer 1

Given the angle:

$\frac{5\pi}{4}$

In order to find the positive and negative coterminal angles to the given angle, you can add and subtract 2π radians

Hence,

Positive co-terminal angle would be:

$\begin{gathered} \frac{5\pi}{4}+2\pi \\ =\frac{5\pi+8\pi}{4} \\ =\frac{13\pi}{4} \end{gathered}$

Negative co-terminal angle would be:

$\begin{gathered} \frac{5\pi}{4}-2\pi \\ =\frac{5\pi-8\pi}{4} \\ =\frac{-3\pi}{4} \end{gathered}$

Therefore, the Positive and Negative coterminal angles are:

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