Trigonometry Examples

$\frac{37 π}{6}$

Step 1

Find an angle that is positive, less than $2 π$ , and coterminal with $\frac{37 π}{6}$ .

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Step 1.1

Subtract $2 π$ from $\frac{37 π}{6}$ .

$\frac{37 π}{6} - 2 π$

Step 1.2

The resulting angle of $\frac{25 π}{6}$ is positive, less than $2 π$ , and coterminal with $\frac{37 π}{6}$ .

$\frac{25 π}{6}$

Step 1.3

Subtract $2 π$ from $\frac{25 π}{6}$ .

$\frac{25 π}{6} - 2 π$

Step 1.4

The resulting angle of $\frac{13 π}{6}$ is positive, less than $2 π$ , and coterminal with $\frac{37 π}{6}$ .

$\frac{13 π}{6}$

Step 1.5

Subtract $2 π$ from $\frac{13 π}{6}$ .

$\frac{13 π}{6} - 2 π$

Step 1.6

The resulting angle of $\frac{π}{6}$ is positive, less than $2 π$ , and coterminal with $\frac{37 π}{6}$ .

$\frac{π}{6}$

Step 2

Since $\frac{π}{6}$ is in the first quadrant, the reference angle is $\frac{π}{6}$ .

$\frac{π}{6}$