Trigonometry Examples

$\sin (x) \cot^{2} (x) - 3 \sin (x) = 0$

Step 1

Simplify $\sin (x) \cot^{2} (x) - 3 \sin (x)$ .

Tap for more steps...

Step 1.1

Simplify each term.

Tap for more steps...

Step 1.1.1

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

$\sin (x) {(\frac{\cos (x)}{\sin (x)})}^{2} - 3 \sin (x) = 0$

Step 1.1.2

Apply the product rule to $\frac{\cos (x)}{\sin (x)}$ .

$\sin (x) \frac{\cos^{2} (x)}{\sin^{2} (x)} - 3 \sin (x) = 0$

Step 1.1.3

Cancel the common factor of $\sin (x)$ .

Tap for more steps...

Step 1.1.3.1

Factor $\sin (x)$ out of $\sin^{2} (x)$ .

$\sin (x) \frac{\cos^{2} (x)}{\sin (x) \sin (x)} - 3 \sin (x) = 0$

Step 1.1.3.2

Cancel the common factor.

$\sin (x) \frac{\cos^{2} (x)}{\sin (x) \sin (x)} - 3 \sin (x) = 0$

Step 1.1.3.3

Rewrite the expression.

$\frac{\cos^{2} (x)}{\sin (x)} - 3 \sin (x) = 0$

Step 1.2

Simplify each term.

Tap for more steps...

Step 1.2.1

Factor $\cos (x)$ out of $\cos^{2} (x)$ .

$\frac{\cos (x) \cos (x)}{\sin (x)} - 3 \sin (x) = 0$

Step 1.2.2

Separate fractions.

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

Step 1.2.3

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

$\frac{\cos (x)}{1} \cot (x) - 3 \sin (x) = 0$

Step 1.2.4

Divide $\cos (x)$ by $1$ .

$\cos (x) \cot (x) - 3 \sin (x) = 0$

Step 2

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

$x = \frac{π}{6} + π n, \frac{5 π}{6} + π n$ , for any integer $n$

Step 3