Trigonometry Examples

$\tan (\frac{θ}{2}) - \sin (θ) = 0$

Step 1

Simplify $\tan (\frac{θ}{2}) - \sin (θ)$ .

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Step 1.1

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

$\frac{\sin (\frac{θ}{2})}{\cos (\frac{θ}{2})} - \sin (θ) = 0$

Step 1.2

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

$\tan (\frac{θ}{2}) - \sin (θ) = 0$

Step 2

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

$θ = 2 π n, \frac{π}{2} + 2 π n, \frac{3 π}{2} + 2 π n$ , for any integer $n$

Step 3