Precalculus Examples

$\cos (t) - \cos (- t) + \sin (t) - \sin (- t)$

Step 1

Simplify each term.

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Step 1.1

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

$\cos (t) - \cos (t) + \sin (t) - \sin (- t)$

Step 1.2

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

$\cos (t) - \cos (t) + \sin (t) - - \sin (t)$

Step 1.3

Multiply $- - \sin (t)$ .

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Step 1.3.1

Multiply $- 1$ by $- 1$ .

$\cos (t) - \cos (t) + \sin (t) + 1 \sin (t)$

Step 1.3.2

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

$\cos (t) - \cos (t) + \sin (t) + \sin (t)$

Step 2

Simplify by adding terms.

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Step 2.1

Subtract $\cos (t)$ from $\cos (t)$ .

$0 + \sin (t) + \sin (t)$

Step 2.2

Add $0$ and $\sin (t)$ .

$\sin (t) + \sin (t)$

Step 2.3

Add $\sin (t)$ and $\sin (t)$ .

$2 \sin (t)$