Trigonometry Examples

$y = \frac{15}{\tan (30)}$

Step 1

Simplify $\frac{15}{\tan (30)}$ .

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Step 1.1

Separate fractions.

$y = \frac{15}{1} \cdot \frac{1}{\tan (30)}$

Step 1.2

Rewrite $\tan (30)$ in terms of sines and cosines.

$y = \frac{15}{1} \cdot \frac{1}{\frac{\sin (30)}{\cos (30)}}$

Step 1.3

Multiply by the reciprocal of the fraction to divide by $\frac{\sin (30)}{\cos (30)}$ .

$y = \frac{15}{1} \cdot \frac{\cos (30)}{\sin (30)}$

Step 1.4

Convert from $\frac{\cos (30)}{\sin (30)}$ to $\cot (30)$ .

$y = \frac{15}{1} \cot (30)$

Step 1.5

Divide $15$ by $1$ .

$y = 15 \cot (30)$

Step 1.6

The exact value of $\cot (30)$ is $\sqrt{3}$ .

$y = 15 \sqrt{3}$

Step 2

The result can be shown in multiple forms.

Exact Form:

$y = 15 \sqrt{3}$

Decimal Form:

$y = 25.98076211 \dots$