Precalculus Examples

$\cos (θ - \frac{π}{3})$

Step 1

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

$\cos (θ) \cos (\frac{π}{3}) + \sin (θ) \sin (\frac{π}{3})$

Step 2

Simplify each term.

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Step 2.1

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

$\cos (θ) \frac{1}{2} + \sin (θ) \sin (\frac{π}{3})$

Step 2.2

Combine $\cos (θ)$ and $\frac{1}{2}$ .

$\frac{\cos (θ)}{2} + \sin (θ) \sin (\frac{π}{3})$

Step 2.3

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

$\frac{\cos (θ)}{2} + \sin (θ) \frac{\sqrt{3}}{2}$

Step 2.4

Combine $\sin (θ)$ and $\frac{\sqrt{3}}{2}$ .

$\frac{\cos (θ)}{2} + \frac{\sin (θ) \sqrt{3}}{2}$