Trigonometry Examples

$\frac{23 π}{4}$

Step 1

Find an angle that is positive, less than $2 π$ , and coterminal with $\frac{23 π}{4}$ .

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Step 1.1

Subtract $2 π$ from $\frac{23 π}{4}$ .

$\frac{23 π}{4} - 2 π$

Step 1.2

The resulting angle of $\frac{15 π}{4}$ is positive, less than $2 π$ , and coterminal with $\frac{23 π}{4}$ .

$\frac{15 π}{4}$

Step 1.3

Subtract $2 π$ from $\frac{15 π}{4}$ .

$\frac{15 π}{4} - 2 π$

Step 1.4

The resulting angle of $\frac{7 π}{4}$ is positive, less than $2 π$ , and coterminal with $\frac{23 π}{4}$ .

$\frac{7 π}{4}$

Step 2

Since the angle $\frac{7 π}{4}$ is in the fourth quadrant, subtract $\frac{7 π}{4}$ from $2 π$ .

$2 π - \frac{7 π}{4}$

Step 3

Simplify the result.

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Step 3.1

To write $2 π$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$2 π \cdot \frac{4}{4} - \frac{7 π}{4}$

Step 3.2

Combine fractions.

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Step 3.2.1

Combine $2 π$ and $\frac{4}{4}$ .

$\frac{2 π \cdot 4}{4} - \frac{7 π}{4}$

Step 3.2.2

Combine the numerators over the common denominator.

$\frac{2 π \cdot 4 - 7 π}{4}$

Step 3.3

Simplify the numerator.

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Step 3.3.1

Multiply $4$ by $2$ .

$\frac{8 π - 7 π}{4}$

Step 3.3.2

Subtract $7 π$ from $8 π$ .

$\frac{π}{4}$