Trigonometry Examples

$- \frac{\sqrt{3}}{3} \cdot (\sin (x) \sec (x)) = 1$

Step 1

Simplify $- \frac{\sqrt{3}}{3} \cdot (\sin (x) \sec (x))$ .

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Step 1.1

Rewrite $\sec (x)$ in terms of sines and cosines.

$- \frac{\sqrt{3}}{3} \cdot (\sin (x) \frac{1}{\cos (x)}) = 1$

Step 1.2

Combine $\sin (x)$ and $\frac{1}{\cos (x)}$ .

$- \frac{\sqrt{3}}{3} \cdot \frac{\sin (x)}{\cos (x)} = 1$

Step 1.3

Multiply $\frac{\sin (x)}{\cos (x)}$ by $\frac{\sqrt{3}}{3}$ .

$- \frac{\sin (x) \sqrt{3}}{\cos (x) \cdot 3} = 1$

Step 1.4

Move $3$ to the left of $\cos (x)$ .

$- \frac{\sin (x) \sqrt{3}}{3 \cdot \cos (x)} = 1$

Step 1.5

Separate fractions.

$- (\frac{\sqrt{3}}{3} \cdot \frac{\sin (x)}{\cos (x)}) = 1$

Step 1.6

Convert from $\frac{\sin (x)}{\cos (x)}$ to $\tan (x)$ .

$- (\frac{\sqrt{3}}{3} \tan (x)) = 1$

Step 1.7

Combine $\frac{\sqrt{3}}{3}$ and $\tan (x)$ .

$- \frac{\sqrt{3} \tan (x)}{3} = 1$

Step 2

Graph each side of the equation. The solution is the x-value of the point of intersection.

$x = \frac{2 π}{3} + π n$ , for any integer $n$

Step 3