Trigonometry Examples

\sin (\frac{5}{3} \cdot π)

$\sin (\frac{5}{3} \cdot π)$

Step 1

Combine

\frac{5}{3}

$\frac{5}{3}$ and

π

$π$ .

\sin (\frac{5 π}{3})

$\sin (\frac{5 π}{3})$

Step 2

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})

$- \sin (\frac{π}{3})$

Step 3

The exact value of

\sin (\frac{π}{3})

$\sin (\frac{π}{3})$ is

\frac{\sqrt{3}}{2}

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

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

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

Step 4

The result can be shown in multiple forms.

Exact Form:

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

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

Decimal Form:

- 0.86602540 \dots

$- 0.86602540 \dots$