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

Multiply $2 (- \frac{π}{3})$ .

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Step 2.1

Multiply $- 1$ by $2$ .

$\cos (- 2 \frac{π}{3})$

Step 2.2

Combine $- 2$ and $\frac{π}{3}$ .

$\cos (\frac{- 2 π}{3})$

Step 3

Move the negative in front of the fraction.

$\cos (- \frac{2 π}{3})$

Step 4

Add full rotations of $2 π$ until the angle is greater than or equal to $0$ and less than $2 π$ .

$\cos (\frac{4 π}{3})$

Step 5

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 third quadrant.

$- \cos (\frac{π}{3})$

Step 6

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

$- \frac{1}{2}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$- \frac{1}{2}$

Decimal Form:

$- 0.5$