Trigonometry Examples

$\cos (2 \arcsin (\frac{\sqrt{3}}{2}))$

Step 1

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

$\cos (2 \frac{π}{3})$

Step 2

Combine $2$ and $\frac{π}{3}$ .

$\cos (\frac{2 π}{3})$

Step 3

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

$- \cos (\frac{π}{3})$

Step 4

The exact value of $\cos (\frac{π}{3})$ is $\frac{1}{2}$ .

$- \frac{1}{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$- \frac{1}{2}$

Decimal Form:

$- 0.5$