Calculus Examples

$\frac{4 π}{3}$

Step 1

Evaluate $\cos (\frac{4 π}{3})$ .

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Step 1.1

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. Make the expression negative because cosine is negative in the third quadrant.

$- \cos (\frac{π}{3})$

Step 1.2

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

$- \frac{1}{2}$

Step 2

Evaluate $\sin (\frac{4 π}{3})$ .

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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 third quadrant.

$- \sin (\frac{π}{3})$

Step 2.2

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

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

Step 3

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

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