Trigonometry Examples

$- 45 + \frac{59}{60} + \frac{34}{3600}$

Step 1

To convert degrees to radians, multiply by $\frac{π}{180 °}$ , since a full circle is $360 °$ or $2 π$ radians.

$- 45 + \frac{59}{60} + \frac{34}{3600 °} \cdot \frac{π}{180 °}$ radians

Step 2

Simplify each term.

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Step 2.1

Cancel the common factor of $2$ .

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Step 2.1.1

Factor $2$ out of $34$ .

$- 45 + \frac{59}{60} + \frac{2 (17)}{3600} \cdot \frac{π}{180}$ radians

Step 2.1.2

Factor $2$ out of $180$ .

$- 45 + \frac{59}{60} + \frac{2 \cdot 17}{3600} \cdot \frac{π}{2 \cdot 90}$ radians

Step 2.1.3

Cancel the common factor.

$- 45 + \frac{59}{60} + \frac{2 \cdot 17}{3600} \cdot \frac{π}{2 \cdot 90}$ radians

Step 2.1.4

Rewrite the expression.

$- 45 + \frac{59}{60} + \frac{17}{3600} \cdot \frac{π}{90}$ radians

Step 2.2

Multiply $\frac{17}{3600}$ by $\frac{π}{90}$ .

$- 45 + \frac{59}{60} + \frac{17 π}{3600 \cdot 90}$ radians

Step 2.3

Multiply $3600$ by $90$ .

$- 45 + \frac{59}{60} + \frac{17 π}{324000}$ radians

Step 3

To write $- 45$ as a fraction with a common denominator, multiply by $\frac{60}{60}$ .

$- 45 \cdot \frac{60}{60} + \frac{59}{60} + \frac{17 π}{324000}$ radians

Step 4

Combine $- 45$ and $\frac{60}{60}$ .

$\frac{- 45 \cdot 60}{60} + \frac{59}{60} + \frac{17 π}{324000}$ radians

Step 5

Combine the numerators over the common denominator.

$\frac{- 45 \cdot 60 + 59}{60} + \frac{17 π}{324000}$ radians

Step 6

Simplify the numerator.

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Step 6.1

Multiply $- 45$ by $60$ .

$\frac{- 2700 + 59}{60} + \frac{17 π}{324000}$ radians

Step 6.2

Add $- 2700$ and $59$ .

$\frac{- 2641}{60} + \frac{17 π}{324000}$ radians

Step 7

Move the negative in front of the fraction.

$- \frac{2641}{60} + \frac{17 π}{324000}$ radians