Trigonometry Examples

$- 5 π$

Step 1

Find an angle that is positive, less than $2 π$ , and coterminal with $- 5 π$ .

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Step 1.1

Add $2 π$ to $- 5 π$ .

$- 5 π + 2 π$

Step 1.2

The resulting angle of $- 3 π$ is coterminal with $- 5 π$ but isn't positive. Repeat the step.

$- 3 π$

Step 1.3

Add $2 π$ to $- 3 π$ .

$- 3 π + 2 π$

Step 1.4

The resulting angle of $- π$ is coterminal with $- 5 π$ but isn't positive. Repeat the step.

$- π$

Step 1.5

Add $2 π$ to $- π$ .

$- π + 2 π$

Step 1.6

The resulting angle of $π$ is positive and coterminal with $- 5 π$ .

$π$

Step 2

Since the angle $π$ is in the second quadrant, subtract $π$ from $π$ .

$π - π$

Step 3

Subtract $π$ from $π$ .

$0$