Trigonometry Examples

$\tan (\frac{x}{2}) \cos (x) = \frac{24}{25}$

Step 1

Simplify $\tan (\frac{x}{2}) \cos (x)$ .

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Step 1.1

Rewrite $\tan (\frac{x}{2})$ in terms of sines and cosines.

$\frac{\sin (\frac{x}{2})}{\cos (\frac{x}{2})} \cos (x) = \frac{24}{25}$

Step 1.2

Combine $\frac{\sin (\frac{x}{2})}{\cos (\frac{x}{2})}$ and $\cos (x)$ .

$\frac{\sin (\frac{x}{2}) \cos (x)}{\cos (\frac{x}{2})} = \frac{24}{25}$

Step 1.3

Separate fractions.

$\frac{\cos (x)}{1} \cdot \frac{\sin (\frac{x}{2})}{\cos (\frac{x}{2})} = \frac{24}{25}$

Step 1.4

Convert from $\frac{\sin (\frac{x}{2})}{\cos (\frac{x}{2})}$ to $\tan (\frac{x}{2})$ .

$\frac{\cos (x)}{1} \tan (\frac{x}{2}) = \frac{24}{25}$

Step 1.5

Divide $\cos (x)$ by $1$ .

$\cos (x) \tan (\frac{x}{2}) = \frac{24}{25}$

Step 2

Graph each side of the equation. The solution is the x-value of the point of intersection.

$x \approx 4.15238015 + 2 π n$ , for any integer $n$

Step 3