Precalculus Examples

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

Step 1

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.

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

Step 2

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

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

Step 3

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

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

Step 4

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$0.15891862 \dots$