Trigonometry Examples

$\frac{49 π}{2}$

Step 1

Find an angle that is positive, less than

$2 π$ , and coterminal with

$\frac{49 π}{2}$ .

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Step 1.1

Subtract

$2 π$ from

$\frac{49 π}{2}$ until the angle falls between

$0$ and

$2 π$ . In this case,

$2 π$ needs to be subtracted

$12$ times.

$\frac{49 π}{2} + 12 (2 π)$

Step 1.2

Simplify.

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Step 1.2.1

Multiply

$2$ by

$- 12$ .

$\frac{49 π}{2} - 24 π$

Step 1.2.2

To write

$- 24 π$ as a fraction with a common denominator, multiply by

$\frac{2}{2}$ .

$\frac{49 π}{2} - 24 π \cdot \frac{2}{2}$

Step 1.2.3

Combine fractions.

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Step 1.2.3.1

Combine

$- 24 π$ and

$\frac{2}{2}$ .

$\frac{49 π}{2} + \frac{- 24 π \cdot 2}{2}$

Step 1.2.3.2

Combine the numerators over the common denominator.

$\frac{49 π - 24 π \cdot 2}{2}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply

$2$ by

$- 24$ .

$\frac{49 π - 48 π}{2}$

Step 1.2.4.2

Subtract

$48 π$ from

$49 π$ .

$\frac{π}{2}$

Step 2

Since

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

$\frac{π}{2}$ .

$\frac{π}{2}$