Precalculus Examples

\frac{5 π}{3}

$\frac{5 π}{3}$

Step 1

Evaluate

\cos (\frac{5 π}{3})

$\cos (\frac{5 π}{3})$ .

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Step 1.1

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant.

\cos (\frac{π}{3})

$\cos (\frac{π}{3})$

Step 1.2

The exact value of

\cos (\frac{π}{3})

$\cos (\frac{π}{3})$ is

\frac{1}{2}

$\frac{1}{2}$ .

\frac{1}{2}

$\frac{1}{2}$

\frac{1}{2}

$\frac{1}{2}$

Step 2

Evaluate

\sin (\frac{5 π}{3})

$\sin (\frac{5 π}{3})$ .

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Step 2.1

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 2.2

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}

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

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

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

Step 3

Set up the coordinates

(\cos (θ), \sin (θ))

$(\cos (θ), \sin (θ))$ .

(\frac{1}{2}, - \frac{\sqrt{3}}{2})

$(\frac{1}{2}, - \frac{\sqrt{3}}{2})$

\frac{5 π}{3}

$\frac{5 π}{3}$

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