Trigonometry Examples

$- \frac{5 π}{4}$

Step 1

Find an angle that is positive, less than $2 π$ , and coterminal with $- \frac{5 π}{4}$ .

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Step 1.1

Add $2 π$ to $- \frac{5 π}{4}$ .

$- \frac{5 π}{4} + 2 π$

Step 1.2

The resulting angle of $\frac{3 π}{4}$ is positive and coterminal with $- \frac{5 π}{4}$ .

$\frac{3 π}{4}$

Step 2

Since the angle $\frac{3 π}{4}$ is in the second quadrant, subtract $\frac{3 π}{4}$ from $π$ .

$π - \frac{3 π}{4}$

Step 3

Simplify the result.

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Step 3.1

To write $π$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$π \cdot \frac{4}{4} - \frac{3 π}{4}$

Step 3.2

Combine fractions.

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Step 3.2.1

Combine $π$ and $\frac{4}{4}$ .

$\frac{π \cdot 4}{4} - \frac{3 π}{4}$

Step 3.2.2

Combine the numerators over the common denominator.

$\frac{π \cdot 4 - 3 π}{4}$

Step 3.3

Simplify the numerator.

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Step 3.3.1

Move $4$ to the left of $π$ .

$\frac{4 \cdot π - 3 π}{4}$

Step 3.3.2

Subtract $3 π$ from $4 π$ .

$\frac{π}{4}$