Trigonometry Examples

$\sin (- x) \cos (- x) \csc (- x)$

Step 1

Since $\sin (- x)$ is an odd function, rewrite $\sin (- x)$ as $- \sin (x)$ .

$- \sin (x) \cos (- x) \csc (- x)$

Step 2

Since $\cos (- x)$ is an even function, rewrite $\cos (- x)$ as $\cos (x)$ .

$- \sin (x) \cos (x) \csc (- x)$

Step 3

Since $\csc (- x)$ is an odd function, rewrite $\csc (- x)$ as $- \csc (x)$ .

$- \sin (x) \cos (x) (- \csc (x))$

Step 4

Rewrite $\csc (x)$ in terms of sines and cosines.

$- \sin (x) \cos (x) (- \frac{1}{\sin (x)})$

Step 5

Cancel the common factor of $\sin (x)$ .

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Step 5.1

Move the leading negative in $- \frac{1}{\sin (x)}$ into the numerator.

$- \sin (x) \cos (x) \frac{- 1}{\sin (x)}$

Step 5.2

Factor $\sin (x)$ out of $- \sin (x) \cos (x)$ .

$\sin (x) (- 1 \cos (x)) \frac{- 1}{\sin (x)}$

Step 5.3

Cancel the common factor.

$\sin (x) (- 1 \cos (x)) \frac{- 1}{\sin (x)}$

Step 5.4

Rewrite the expression.

$- 1 \cos (x) \cdot - 1$

Step 6

Multiply.

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Step 6.1

Multiply $- 1$ by $- 1$ .

$1 \cos (x)$

Step 6.2

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

$\cos (x)$