Precalculus Examples

$\frac{19 π}{6}$

Step 1

Evaluate $\cos (\frac{19 π}{6})$ .

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Step 1.1

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

$\cos (\frac{7 π}{6})$

Step 1.2

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.

$- \cos (\frac{π}{6})$

Step 1.3

The exact value of $\cos (\frac{π}{6})$ is $\frac{\sqrt{3}}{2}$ .

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

Step 2

Evaluate $\sin (\frac{19 π}{6})$ .

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Step 2.1

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

$\sin (\frac{7 π}{6})$

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 third quadrant.

$- \sin (\frac{π}{6})$

Step 2.3

The exact value of $\sin (\frac{π}{6})$ is $\frac{1}{2}$ .

$- \frac{1}{2}$

Step 3

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

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