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 $\frac{π}{2}$ .

$\frac{π}{2}$