Trigonometry Examples

$\sin (\arccos (\frac{1}{2}) - \arcsin (\frac{\sqrt{3}}{2}))$

Step 1

Simplify each term.

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Step 1.1

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

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

Step 1.2

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

$\sin (\frac{π}{3} - \frac{π}{3})$

Step 2

Simplify terms.

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Step 2.1

Combine the numerators over the common denominator.

$\sin (\frac{π - π}{3})$

Step 2.2

Subtract $π$ from $π$ .

$\sin (\frac{0}{3})$

Step 2.3

Divide $0$ by $3$ .

$\sin (0)$

Step 3

The exact value of $\sin (0)$ is $0$ .

$0$