Trigonometry Examples

$\tan (t) - \sin (2 t) = - \tan (t) \cos (2 t)$

Step 1

Simplify $\tan (t) - \sin (2 t)$ .

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Step 1.1

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

$\frac{\sin (t)}{\cos (t)} - \sin (2 t) = - \tan (t) \cos (2 t)$

Step 1.2

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

$\tan (t) - \sin (2 t) = - \tan (t) \cos (2 t)$

Step 2

Simplify $- \tan (t) \cos (2 t)$ .

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Step 2.1

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

$\tan (t) - \sin (2 t) = - \frac{\sin (t)}{\cos (t)} \cos (2 t)$

Step 2.2

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

$\tan (t) - \sin (2 t) = - \frac{\cos (2 t) \sin (t)}{\cos (t)}$

Step 2.3

Separate fractions.

$\tan (t) - \sin (2 t) = - (\frac{\sin (t)}{1} \cdot \frac{\cos (2 t)}{\cos (t)})$

Step 2.4

Rewrite $\frac{\cos (2 t)}{\cos (t)}$ as a product.

$\tan (t) - \sin (2 t) = - (\frac{\sin (t)}{1} (\cos (2 t) \frac{1}{\cos (t)}))$

Step 2.5

Write $\cos (2 t)$ as a fraction with denominator $1$ .

$\tan (t) - \sin (2 t) = - (\frac{\sin (t)}{1} (\frac{\cos (2 t)}{1} \cdot \frac{1}{\cos (t)}))$

Step 2.6

Simplify.

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Step 2.6.1

Divide $\cos (2 t)$ by $1$ .

$\tan (t) - \sin (2 t) = - (\frac{\sin (t)}{1} (\cos (2 t) \frac{1}{\cos (t)}))$

Step 2.6.2

Convert from $\frac{1}{\cos (t)}$ to $\sec (t)$ .

$\tan (t) - \sin (2 t) = - (\frac{\sin (t)}{1} (\cos (2 t) \sec (t)))$

Step 2.7

Divide $\sin (t)$ by $1$ .

$\tan (t) - \sin (2 t) = - \sin (t) \cos (2 t) \sec (t)$

Step 3

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

$t \approx - 0.1, 0.1, - \frac{1}{5}, \frac{1}{5}, - 0.3, 0.3, \frac{2}{5}$

Step 4