Precalculus Examples

$\frac{11 π}{4}$

Step 1

Evaluate $\cos (\frac{11 π}{4})$ .

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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 $2 π$ .

$\cos (\frac{3 π}{4})$

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 second quadrant.

$- \cos (\frac{π}{4})$

Step 1.3

The exact value of $\cos (\frac{π}{4})$ is $\frac{\sqrt{2}}{2}$ .

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

Step 2

Evaluate $\sin (\frac{11 π}{4})$ .

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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 $2 π$ .

$\sin (\frac{3 π}{4})$

Step 2.2

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

$\sin (\frac{π}{4})$

Step 2.3

The exact value of $\sin (\frac{π}{4})$ is $\frac{\sqrt{2}}{2}$ .

$\frac{\sqrt{2}}{2}$

Step 3

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

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