Trigonometry Examples

$- \frac{35 π}{4}$

Step 1

Find an angle that is positive, less than $2 π$ , and coterminal with $- \frac{35 π}{4}$ .

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Step 1.1

Add $2 π$ to $- \frac{35 π}{4}$ .

$- \frac{35 π}{4} + 2 π$

Step 1.2

The resulting angle of $- \frac{27 π}{4}$ is coterminal with $- \frac{35 π}{4}$ but isn't positive. Repeat the step.

$- \frac{27 π}{4}$

Step 1.3

Add $2 π$ to $- \frac{27 π}{4}$ .

$- \frac{27 π}{4} + 2 π$

Step 1.4

The resulting angle of $- \frac{19 π}{4}$ is coterminal with $- \frac{35 π}{4}$ but isn't positive. Repeat the step.

$- \frac{19 π}{4}$

Step 1.5

Add $2 π$ to $- \frac{19 π}{4}$ .

$- \frac{19 π}{4} + 2 π$

Step 1.6

The resulting angle of $- \frac{11 π}{4}$ is coterminal with $- \frac{35 π}{4}$ but isn't positive. Repeat the step.

$- \frac{11 π}{4}$

Step 1.7

Add $2 π$ to $- \frac{11 π}{4}$ .

$- \frac{11 π}{4} + 2 π$

Step 1.8

The resulting angle of $- \frac{3 π}{4}$ is coterminal with $- \frac{35 π}{4}$ but isn't positive. Repeat the step.

$- \frac{3 π}{4}$

Step 1.9

Add $2 π$ to $- \frac{3 π}{4}$ .

$- \frac{3 π}{4} + 2 π$

Step 1.10

The resulting angle of $\frac{5 π}{4}$ is positive and coterminal with $- \frac{35 π}{4}$ .

$\frac{5 π}{4}$

Step 2

Since the angle $π$ is in the third quadrant, subtract $π$ from $\frac{5 π}{4}$ .

$\frac{5 π}{4} - π$

Step 3

Simplify the result.

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Step 3.1

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

$\frac{5 π}{4} - π \cdot \frac{4}{4}$

Step 3.2

Combine fractions.

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Step 3.2.1

Combine $- π$ and $\frac{4}{4}$ .

$\frac{5 π}{4} + \frac{- π \cdot 4}{4}$

Step 3.2.2

Combine the numerators over the common denominator.

$\frac{5 π - π \cdot 4}{4}$

Step 3.3

Simplify the numerator.

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Step 3.3.1

Multiply $4$ by $- 1$ .

$\frac{5 π - 4 π}{4}$

Step 3.3.2

Subtract $4 π$ from $5 π$ .

$\frac{π}{4}$