Precalculus Examples

$x = 20 \sin (300)$

Step 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 fourth quadrant.

$x = 20 (- \sin (60))$

Step 2

The exact value of $\sin (60)$ is $\frac{\sqrt{3}}{2}$ .

$x = 20 (- \frac{\sqrt{3}}{2})$

Step 3

Cancel the common factor of $2$ .

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Step 3.1

Move the leading negative in $- \frac{\sqrt{3}}{2}$ into the numerator.

$x = 20 \frac{- \sqrt{3}}{2}$

Step 3.2

Factor $2$ out of $20$ .

$x = 2 (10) \frac{- \sqrt{3}}{2}$

Step 3.3

Cancel the common factor.

$x = 2 \cdot 10 \frac{- \sqrt{3}}{2}$

Step 3.4

Rewrite the expression.

$x = 10 (- \sqrt{3})$

Step 4

Multiply $- 1$ by $10$ .

$x = - 10 \sqrt{3}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = - 10 \sqrt{3}$

Decimal Form:

$x = - 17.32050807 \dots$