Trigonometry Examples

$x \tan (32.333) - \tan (28.833) = 200 \tan (23.833)$

Step 1

Add $\tan (28.833)$ to both sides of the equation.

$x \tan (32.333) = 200 \tan (23.833) + \tan (28.833)$

Step 2

Divide each term in $x \tan (32.333) = 200 \tan (23.833) + \tan (28.833)$ by $\tan (32.333)$ and simplify.

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Step 2.1

Divide each term in $x \tan (32.333) = 200 \tan (23.833) + \tan (28.833)$ by $\tan (32.333)$ .

$\frac{x \tan (32.333)}{\tan (32.333)} = \frac{200 \tan (23.833)}{\tan (32.333)} + \frac{\tan (28.833)}{\tan (32.333)}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $\tan (32.333)$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{x \tan (32.333)}{\tan (32.333)} = \frac{200 \tan (23.833)}{\tan (32.333)} + \frac{\tan (28.833)}{\tan (32.333)}$

Step 2.2.1.2

Divide $x$ by $1$ .

$x = \frac{200 \tan (23.833)}{\tan (32.333)} + \frac{\tan (28.833)}{\tan (32.333)}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Simplify each term.

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Step 2.3.1.1

Separate fractions.

$x = \frac{200}{1} \cdot \frac{\tan (23.833)}{\tan (32.333)} + \frac{\tan (28.833)}{\tan (32.333)}$

Step 2.3.1.2

Rewrite $\tan (32.333)$ in terms of sines and cosines.

$x = \frac{200}{1} \cdot \frac{\tan (23.833)}{\frac{\sin (32.333)}{\cos (32.333)}} + \frac{\tan (28.833)}{\tan (32.333)}$

Step 2.3.1.3

Rewrite $\tan (23.833)$ in terms of sines and cosines.

$x = \frac{200}{1} \cdot \frac{\frac{\sin (23.833)}{\cos (23.833)}}{\frac{\sin (32.333)}{\cos (32.333)}} + \frac{\tan (28.833)}{\tan (32.333)}$

Step 2.3.1.4

Multiply by the reciprocal of the fraction to divide by $\frac{\sin (32.333)}{\cos (32.333)}$ .

$x = \frac{200}{1} (\frac{\sin (23.833)}{\cos (23.833)} \cdot \frac{\cos (32.333)}{\sin (32.333)}) + \frac{\tan (28.833)}{\tan (32.333)}$

Step 2.3.1.5

Simplify.

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Step 2.3.1.5.1

Convert from $\frac{\sin (23.833)}{\cos (23.833)}$ to $\tan (23.833)$ .

$x = \frac{200}{1} (\tan (23.833) \frac{\cos (32.333)}{\sin (32.333)}) + \frac{\tan (28.833)}{\tan (32.333)}$

Step 2.3.1.5.2

Convert from $\frac{\cos (32.333)}{\sin (32.333)}$ to $\cot (32.333)$ .

$x = \frac{200}{1} (\tan (23.833) \cot (32.333)) + \frac{\tan (28.833)}{\tan (32.333)}$

Step 2.3.1.6

Divide $200$ by $1$ .

$x = 200 (\tan (23.833) \cot (32.333)) + \frac{\tan (28.833)}{\tan (32.333)}$

Step 2.3.1.7

Rewrite $\tan (32.333)$ in terms of sines and cosines.

$x = 200 \tan (23.833) \cot (32.333) + \frac{\tan (28.833)}{\frac{\sin (32.333)}{\cos (32.333)}}$

Step 2.3.1.8

Rewrite $\tan (28.833)$ in terms of sines and cosines.

$x = 200 \tan (23.833) \cot (32.333) + \frac{\frac{\sin (28.833)}{\cos (28.833)}}{\frac{\sin (32.333)}{\cos (32.333)}}$

Step 2.3.1.9

Multiply by the reciprocal of the fraction to divide by $\frac{\sin (32.333)}{\cos (32.333)}$ .

$x = 200 \tan (23.833) \cot (32.333) + \frac{\sin (28.833)}{\cos (28.833)} \cdot \frac{\cos (32.333)}{\sin (32.333)}$

Step 2.3.1.10

Simplify.

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Step 2.3.1.10.1

Convert from $\frac{\sin (28.833)}{\cos (28.833)}$ to $\tan (28.833)$ .

$x = 200 \tan (23.833) \cot (32.333) + \tan (28.833) \frac{\cos (32.333)}{\sin (32.333)}$

Step 2.3.1.10.2

Convert from $\frac{\cos (32.333)}{\sin (32.333)}$ to $\cot (32.333)$ .

$x = 200 \tan (23.833) \cot (32.333) + \tan (28.833) \cot (32.333)$

Step 3

The result can be shown in multiple forms.

Exact Form:

$x = 200 \tan (23.833) \cot (32.333) + \tan (28.833) \cot (32.333)$

Decimal Form:

$x = 140.44460092 \dots$