Trigonometry Examples

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

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

Step 1

Simplify each term.

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Step 1.1

The exact value of

arccos (\frac{1}{2})

$\arccos (\frac{1}{2})$ is

\frac{π}{3}

$\frac{π}{3}$ .

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

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

Step 1.2

The exact value of

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

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

\frac{π}{3}

$\frac{π}{3}$ .

sin (\frac{π}{3} - \frac{π}{3})

$\sin (\frac{π}{3} - \frac{π}{3})$

sin (\frac{π}{3} - \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})

$\sin (\frac{π - π}{3})$

Step 2.2

Subtract

π

$π$ from

π

$π$ .

sin (\frac{0}{3})

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

Step 2.3

Divide

0

$0$ by

3

$3$ .

sin (0)

$\sin (0)$

sin (0)

$\sin (0)$

Step 3

The exact value of

sin (0)

$\sin (0)$ is

0

$0$ .

0

$0$