Trigonometry Examples

$- \frac{31 π}{4}$

Step 1

Find an angle that is positive, less than $2 π$ , and coterminal with $- \frac{31 π}{4}$ .

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Step 1.1

Add $2 π$ to $- \frac{31 π}{4}$ .

$- \frac{31 π}{4} + 2 π$

Step 1.2

The resulting angle of $- \frac{23 π}{4}$ is coterminal with $- \frac{31 π}{4}$ but isn't positive. Repeat the step.

$- \frac{23 π}{4}$

Step 1.3

Add $2 π$ to $- \frac{23 π}{4}$ .

$- \frac{23 π}{4} + 2 π$

Step 1.4

The resulting angle of $- \frac{15 π}{4}$ is coterminal with $- \frac{31 π}{4}$ but isn't positive. Repeat the step.

$- \frac{15 π}{4}$

Step 1.5

Add $2 π$ to $- \frac{15 π}{4}$ .

$- \frac{15 π}{4} + 2 π$

Step 1.6

The resulting angle of $- \frac{7 π}{4}$ is coterminal with $- \frac{31 π}{4}$ but isn't positive. Repeat the step.

$- \frac{7 π}{4}$

Step 1.7

Add $2 π$ to $- \frac{7 π}{4}$ .

$- \frac{7 π}{4} + 2 π$

Step 1.8

The resulting angle of $\frac{π}{4}$ is positive and coterminal with $- \frac{31 π}{4}$ .

$\frac{π}{4}$

Step 2

Since $\frac{π}{4}$ is in the first quadrant, the reference angle is $\frac{π}{4}$ .

$\frac{π}{4}$