Trigonometry Examples

$\sin (210)$

Step 1

The complement of $\sin (210)$ is the angle that when added to $\sin (210)$ forms a right angle ( $90 °$ ).

$90 ° - \sin (210)$

Step 2

Simplify each term.

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Step 2.1

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. Make the expression negative because sine is negative in the third quadrant.

Step 2.2

The exact value of $\sin (30)$ is $\frac{1}{2}$ .

$90 + \frac{1}{2 °}$

Step 2.3

Multiply $- - \frac{1}{2}$ .

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Step 2.3.1

Multiply $- 1$ by $- 1$ .

Step 2.3.2

Multiply $\frac{1}{2}$ by $1$ .

$90 + \frac{1}{2 °}$

Step 3

To write $90$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$90 \cdot \frac{2}{2} + \frac{1}{2 °}$

Step 4

Combine $90$ and $\frac{2}{2}$ .

$\frac{90 \cdot 2}{2} + \frac{1}{2 °}$

Step 5

Combine the numerators over the common denominator.

$\frac{90 \cdot 2 + 1}{2 °}$

Step 6

Simplify the numerator.

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Step 6.1

Multiply $90$ by $2$ .

$\frac{180 + 1}{2 °}$

Step 6.2

Add $180$ and $1$ .

$\frac{181}{2 °}$