Trigonometry Examples

$\sin (2 \arccos (- \frac{\sqrt{3}}{2}))$

Step 1

The exact value of $\arccos (- \frac{\sqrt{3}}{2})$ is $\frac{5 π}{6}$ .

$\sin (2 \frac{5 π}{6})$

Step 2

Cancel the common factor of $2$ .

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Step 2.1

Factor $2$ out of $6$ .

$\sin (2 \frac{5 π}{2 (3)})$

Step 2.2

Cancel the common factor.

$\sin (2 \frac{5 π}{2 \cdot 3})$

Step 2.3

Rewrite the expression.

$\sin (\frac{5 π}{3})$

Step 3

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.

$- \sin (\frac{π}{3})$

Step 4

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

$- \frac{\sqrt{3}}{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$- \frac{\sqrt{3}}{2}$

Decimal Form:

$- 0.86602540 \dots$