Trigonometry Examples

$3 \sin (45) - 4 \tan (\frac{π}{6})$

Step 1

The exact value of $\sin (45)$ is $\frac{\sqrt{2}}{2}$ .

$3 \frac{\sqrt{2}}{2} - 4 \tan (\frac{π}{6})$

Step 2

Combine $3$ and $\frac{\sqrt{2}}{2}$ .

$\frac{3 \sqrt{2}}{2} - 4 \tan (\frac{π}{6})$

Step 3

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

$\frac{3 \sqrt{2}}{2} - 4 \frac{\sqrt{3}}{3}$

Step 4

Combine $- 4$ and $\frac{\sqrt{3}}{3}$ .

$\frac{3 \sqrt{2}}{2} + \frac{- 4 \sqrt{3}}{3}$

Step 5

Move the negative in front of the fraction.

$\frac{3 \sqrt{2}}{2} - \frac{4 \sqrt{3}}{3}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{3 \sqrt{2}}{2} - \frac{4 \sqrt{3}}{3}$

Decimal Form:

$- 0.18808073 \dots$