Precalculus Examples

$- \frac{π}{3}$

Step 1

Evaluate $\cos (- \frac{π}{3})$ .

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Step 1.1

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

$\cos (\frac{5 π}{3})$

Step 1.2

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

$\cos (\frac{π}{3})$

Step 1.3

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

$\frac{1}{2}$

Step 2

Evaluate $\sin (- \frac{π}{3})$ .

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Step 2.1

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

$\sin (\frac{5 π}{3})$

Step 2.2

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.

$- \sin (\frac{π}{3})$

Step 2.3

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

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

Step 3

Set up the coordinates $(\cos (θ), \sin (θ))$ .

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