Trigonometry Examples

$x \tan (46 °) = \tan (24 °) + 497 + \tan (24 °)$

Step 1

Add $\tan (24 °)$ and $\tan (24 °)$ .

$x \tan (46 °) = 497 + 2 \tan (24 °)$

Step 2

Divide each term in $x \tan (46 °) = 497 + 2 \tan (24 °)$ by $\tan (46 °)$ and simplify.

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Step 2.1

Divide each term in $x \tan (46 °) = 497 + 2 \tan (24 °)$ by $\tan (46 °)$ .

$\frac{x \tan (46 °)}{\tan (46 °)} = \frac{497}{\tan (46 °)} + \frac{2 \tan (24 °)}{\tan (46 °)}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $\tan (46 °)$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{x \tan (46 °)}{\tan (46 °)} = \frac{497}{\tan (46 °)} + \frac{2 \tan (24 °)}{\tan (46 °)}$

Step 2.2.1.2

Divide $x$ by $1$ .

$x = \frac{497}{\tan (46 °)} + \frac{2 \tan (24 °)}{\tan (46 °)}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Combine the numerators over the common denominator.

$x = \frac{497 + 2 \tan (24 °)}{\tan (46 °)}$

Step 2.3.2

Simplify each term.

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Step 2.3.2.1

Evaluate $\tan (24 °)$ .

$x = \frac{497 + 2 \cdot 0.44522868}{\tan (46 °)}$

Step 2.3.2.2

Multiply $2$ by $0.44522868$ .

$x = \frac{497 + 0.89045737}{\tan (46 °)}$

Step 2.3.3

Add $497$ and $0.89045737$ .

$x = \frac{497.89045737}{\tan (46 °)}$

Step 2.3.4

Separate fractions.

$x = \frac{497.89045737}{1} \cdot \frac{1}{\tan (46 °)}$

Step 2.3.5

Rewrite $\tan (46 °)$ in terms of sines and cosines.

$x = \frac{497.89045737}{1} \cdot \frac{1}{\frac{\sin (46 °)}{\cos (46 °)}}$

Step 2.3.6

Multiply by the reciprocal of the fraction to divide by $\frac{\sin (46 °)}{\cos (46 °)}$ .

$x = \frac{497.89045737}{1} \cdot \frac{\cos (46 °)}{\sin (46 °)}$

Step 2.3.7

Convert from $\frac{\cos (46 °)}{\sin (46 °)}$ to $\cot (46 °)$ .

$x = \frac{497.89045737}{1} \cot (46 °)$

Step 2.3.8

Divide $497.89045737$ by $1$ .

$x = 497.89045737 \cot (46 °)$

Step 2.3.9

Evaluate $\cot (46 °)$ .

$x = 497.89045737 \cdot 0.96568877$

Step 2.3.10

Multiply $497.89045737$ by $0.96568877$ .

$x = 480.80722576$