Trigonometry Examples

$\cos (\frac{π}{3})$

Step 1

The angle $\frac{π}{3}$ is an angle where the values of the six trigonometric functions are known. Because this is the case, add $0$ to keep the value the same.

$\cos (\frac{π}{3} + 0)$

Step 2

Use the sum formula for cosine to simplify the expression. The formula states that $\cos (A + B) = - (\cos (A) \cos (B) + \sin (A) \sin (B))$ .

$\cos (0) \cdot \cos (\frac{π}{3}) - \sin (0) \cdot \sin (\frac{π}{3})$

Step 3

Remove parentheses.

$\cos (0) \cdot \cos (\frac{π}{3}) - \sin (0) \cdot \sin (\frac{π}{3})$

Step 4

Simplify each term.

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Step 4.1

The exact value of $\cos (0)$ is $1$ .

$1 \cdot \cos (\frac{π}{3}) - \sin (0) \cdot \sin (\frac{π}{3})$

Step 4.2

Multiply $\cos (\frac{π}{3})$ by $1$ .

$\cos (\frac{π}{3}) - \sin (0) \cdot \sin (\frac{π}{3})$

Step 4.3

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

$\frac{1}{2} - \sin (0) \cdot \sin (\frac{π}{3})$

Step 4.4

The exact value of $\sin (0)$ is $0$ .

$\frac{1}{2} - 0 \cdot \sin (\frac{π}{3})$

Step 4.5

Multiply $- 1$ by $0$ .

$\frac{1}{2} + 0 \cdot \sin (\frac{π}{3})$

Step 4.6

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

$\frac{1}{2} + 0 \cdot \frac{\sqrt{3}}{2}$

Step 4.7

Multiply $0$ by $\frac{\sqrt{3}}{2}$ .

$\frac{1}{2} + 0$

Step 5

Add $\frac{1}{2}$ and $0$ .

$\frac{1}{2}$