Trigonometry Examples

$(\frac{3}{2}) \tan (x) = \sqrt{\frac{3}{2}}$

Step 1

Subtract $\sqrt{\frac{3}{2}}$ from both sides of the equation.

$(\frac{3}{2}) \tan (x) - \sqrt{\frac{3}{2}} = 0$

Step 2

Simplify each term.

Tap for more steps...

Step 2.1

Combine $\frac{3}{2}$ and $\tan (x)$ .

$\frac{3 \tan (x)}{2} - \sqrt{\frac{3}{2}} = 0$

Step 2.2

Rewrite $\sqrt{\frac{3}{2}}$ as $\frac{\sqrt{3}}{\sqrt{2}}$ .

$\frac{3 \tan (x)}{2} - \frac{\sqrt{3}}{\sqrt{2}} = 0$

Step 2.3

Multiply $\frac{\sqrt{3}}{\sqrt{2}}$ by $\frac{\sqrt{2}}{\sqrt{2}}$ .

$\frac{3 \tan (x)}{2} - (\frac{\sqrt{3}}{\sqrt{2}} \cdot \frac{\sqrt{2}}{\sqrt{2}}) = 0$

Step 2.4

Combine and simplify the denominator.

Tap for more steps...

Step 2.4.1

Multiply $\frac{\sqrt{3}}{\sqrt{2}}$ by $\frac{\sqrt{2}}{\sqrt{2}}$ .

$\frac{3 \tan (x)}{2} - \frac{\sqrt{3} \sqrt{2}}{\sqrt{2} \sqrt{2}} = 0$

Step 2.4.2

Raise $\sqrt{2}$ to the power of $1$ .

$\frac{3 \tan (x)}{2} - \frac{\sqrt{3} \sqrt{2}}{{\sqrt{2}}^{1} \sqrt{2}} = 0$

Step 2.4.3

Raise $\sqrt{2}$ to the power of $1$ .

$\frac{3 \tan (x)}{2} - \frac{\sqrt{3} \sqrt{2}}{{\sqrt{2}}^{1} {\sqrt{2}}^{1}} = 0$

Step 2.4.4

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{3 \tan (x)}{2} - \frac{\sqrt{3} \sqrt{2}}{{\sqrt{2}}^{1 + 1}} = 0$

Step 2.4.5

Add $1$ and $1$ .

$\frac{3 \tan (x)}{2} - \frac{\sqrt{3} \sqrt{2}}{{\sqrt{2}}^{2}} = 0$

Step 2.4.6

Rewrite ${\sqrt{2}}^{2}$ as $2$ .

Tap for more steps...

Step 2.4.6.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{2}$ as $2^{\frac{1}{2}}$ .

$\frac{3 \tan (x)}{2} - \frac{\sqrt{3} \sqrt{2}}{{(2^{\frac{1}{2}})}^{2}} = 0$

Step 2.4.6.2

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{3 \tan (x)}{2} - \frac{\sqrt{3} \sqrt{2}}{2^{\frac{1}{2} \cdot 2}} = 0$

Step 2.4.6.3

Combine $\frac{1}{2}$ and $2$ .

$\frac{3 \tan (x)}{2} - \frac{\sqrt{3} \sqrt{2}}{2^{\frac{2}{2}}} = 0$

Step 2.4.6.4

Cancel the common factor of $2$ .

Tap for more steps...

Step 2.4.6.4.1

Cancel the common factor.

$\frac{3 \tan (x)}{2} - \frac{\sqrt{3} \sqrt{2}}{2^{\frac{2}{2}}} = 0$

Step 2.4.6.4.2

Rewrite the expression.

$\frac{3 \tan (x)}{2} - \frac{\sqrt{3} \sqrt{2}}{2^{1}} = 0$

Step 2.4.6.5

Evaluate the exponent.

$\frac{3 \tan (x)}{2} - \frac{\sqrt{3} \sqrt{2}}{2} = 0$

Step 2.5

Simplify the numerator.

Tap for more steps...

Step 2.5.1

Combine using the product rule for radicals.

$\frac{3 \tan (x)}{2} - \frac{\sqrt{3 \cdot 2}}{2} = 0$

Step 2.5.2

Multiply $3$ by $2$ .

$\frac{3 \tan (x)}{2} - \frac{\sqrt{6}}{2} = 0$

Step 3

Set the argument in $\tan (x)$ equal to $\frac{π}{2} + π n$ to find where the expression is undefined.

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

Step 4

The equation is undefined where the denominator equals $0$ , the argument of a square root is less than $0$ , or the argument of a logarithm is less than or equal to $0$ .

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

Step 5