Precalculus Examples

$\cos (x - \frac{11 π}{6})$

Step 1

Apply the difference of angles identity $\cos (x - y) = \cos (x) \cos (y) + \sin (x) \sin (y)$ .

$\cos (x) \cos (\frac{11 π}{6}) + \sin (x) \sin (\frac{11 π}{6})$

Step 2

Simplify each term.

Tap for more steps...

Step 2.1

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

$\cos (x) \cos (\frac{π}{6}) + \sin (x) \sin (\frac{11 π}{6})$

Step 2.2

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

$\cos (x) \frac{\sqrt{3}}{2} + \sin (x) \sin (\frac{11 π}{6})$

Step 2.3

Combine $\cos (x)$ and $\frac{\sqrt{3}}{2}$ .

$\frac{\cos (x) \sqrt{3}}{2} + \sin (x) \sin (\frac{11 π}{6})$

Step 2.4

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.

$\frac{\cos (x) \sqrt{3}}{2} + \sin (x) (- \sin (\frac{π}{6}))$

Step 2.5

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

$\frac{\cos (x) \sqrt{3}}{2} + \sin (x) (- \frac{1}{2})$

Step 2.6

Combine $\sin (x)$ and $\frac{1}{2}$ .

$\frac{\cos (x) \sqrt{3}}{2} - \frac{\sin (x)}{2}$