Trigonometry Examples

$\cos (\frac{π}{3}) + \sin (\frac{4 π}{3})$

Step 1

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

$\frac{1}{2} + \sin (\frac{4 π}{3})$

Step 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.

$\frac{1}{2} - \sin (\frac{π}{3})$

Step 3

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

$\frac{1}{2} - \frac{\sqrt{3}}{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{2} - \frac{\sqrt{3}}{2}$

Decimal Form:

$- 0.36602540 \dots$