Trigonometry Examples

$\frac{\sin (- 54)}{\cos (414)} + \tan (234)$

Step 1

Simplify each term.

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Step 1.1

Remove full rotations of $360$ ° until the angle is between $0$ ° and $360$ °.

$\frac{\sin (- 54)}{\cos (54)} + \tan (234)$

Step 1.2

Rewrite $\tan (234)$ in terms of sines and cosines.

$\frac{\sin (- 54)}{\cos (54)} + \frac{\sin (234)}{\cos (234)}$

Step 2

Simplify each term.

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Step 2.1

Rewrite $\frac{\sin (- 54)}{\cos (54)}$ as a product.

$\sin (- 54) \frac{1}{\cos (54)} + \frac{\sin (234)}{\cos (234)}$

Step 2.2

Write $\sin (- 54)$ as a fraction with denominator $1$ .

$\frac{\sin (- 54)}{1} \cdot \frac{1}{\cos (54)} + \frac{\sin (234)}{\cos (234)}$

Step 2.3

Simplify.

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Step 2.3.1

Divide $\sin (- 54)$ by $1$ .

$\sin (- 54) \frac{1}{\cos (54)} + \frac{\sin (234)}{\cos (234)}$

Step 2.3.2

Convert from $\frac{1}{\cos (54)}$ to $\sec (54)$ .

$\sin (- 54) \sec (54) + \frac{\sin (234)}{\cos (234)}$

Step 2.4

Convert from $\frac{\sin (234)}{\cos (234)}$ to $\tan (234)$ .

$\sin (- 54) \sec (54) + \tan (234)$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\sin (- 54) \sec (54) + \tan (234)$

Decimal Form:

$- 4.6629367 \cdot 10^{- 15}$