Trigonometry Examples

$d e = \frac{12}{\tan (19 °)}$

Step 1

Simplify.

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Step 1.1

Separate fractions.

$d e = \frac{12}{1} \cdot \frac{1}{\tan (19 °)}$

Step 1.2

Rewrite $\tan (19 °)$ in terms of sines and cosines.

$d e = \frac{12}{1} \cdot \frac{1}{\frac{\sin (19 °)}{\cos (19 °)}}$

Step 1.3

Multiply by the reciprocal of the fraction to divide by $\frac{\sin (19 °)}{\cos (19 °)}$ .

$d e = \frac{12}{1} \cdot \frac{\cos (19 °)}{\sin (19 °)}$

Step 1.4

Convert from $\frac{\cos (19 °)}{\sin (19 °)}$ to $\cot (19 °)$ .

$d e = \frac{12}{1} \cot (19 °)$

Step 1.5

Divide $12$ by $1$ .

$d e = 12 \cot (19 °)$

Step 1.6

Evaluate $\cot (19 °)$ .

$d e = 12 \cdot 2.90421087$

Step 1.7

Multiply $12$ by $2.90421087$ .

$d e = 34.85053053$

Step 2

Divide each term in $d e = 34.85053053$ by $e$ and simplify.

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Step 2.1

Divide each term in $d e = 34.85053053$ by $e$ .

$\frac{d e}{e} = \frac{34.85053053}{e}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $e$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{d e}{e} = \frac{34.85053053}{e}$

Step 2.2.1.2

Divide $d$ by $1$ .

$d = \frac{34.85053053}{e}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Replace $e$ with an approximation.

$d = \frac{34.85053053}{2.71828182}$

Step 2.3.2

Divide $34.85053053$ by $2.71828182$ .

$d = 12.82079369$