Trigonometry Examples

$\frac{52 π}{5}$

Step 1

Find an angle that is positive, less than $2 π$ , and coterminal with $\frac{52 π}{5}$ .

Tap for more steps...

Step 1.1

Subtract $2 π$ from $\frac{52 π}{5}$ .

$\frac{52 π}{5} - 2 π$

Step 1.2

The resulting angle of $\frac{42 π}{5}$ is positive, less than $2 π$ , and coterminal with $\frac{52 π}{5}$ .

$\frac{42 π}{5}$

Step 1.3

Subtract $2 π$ from $\frac{42 π}{5}$ .

$\frac{42 π}{5} - 2 π$

Step 1.4

The resulting angle of $\frac{32 π}{5}$ is positive, less than $2 π$ , and coterminal with $\frac{52 π}{5}$ .

$\frac{32 π}{5}$

Step 1.5

Subtract $2 π$ from $\frac{32 π}{5}$ .

$\frac{32 π}{5} - 2 π$

Step 1.6

The resulting angle of $\frac{22 π}{5}$ is positive, less than $2 π$ , and coterminal with $\frac{52 π}{5}$ .

$\frac{22 π}{5}$

Step 1.7

Subtract $2 π$ from $\frac{22 π}{5}$ .

$\frac{22 π}{5} - 2 π$

Step 1.8

The resulting angle of $\frac{12 π}{5}$ is positive, less than $2 π$ , and coterminal with $\frac{52 π}{5}$ .

$\frac{12 π}{5}$

Step 1.9

Subtract $2 π$ from $\frac{12 π}{5}$ .

$\frac{12 π}{5} - 2 π$

Step 1.10

The resulting angle of $\frac{2 π}{5}$ is positive, less than $2 π$ , and coterminal with $\frac{52 π}{5}$ .

$\frac{2 π}{5}$

Step 2

Since $\frac{2 π}{5}$ is in the first quadrant, the reference angle is $\frac{2 π}{5}$ .

$\frac{2 π}{5}$