Trigonometry Examples

$\sin (t) - \sin (t) \cos^{2} (t)$

Step 1

Multiply by $1$ .

$\sin (t) \cdot 1 - \sin (t) \cos^{2} (t)$

Step 2

Simplify with factoring out.

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Step 2.1

Factor $\sin (t)$ out of $- \sin (t) \cos^{2} (t)$ .

$\sin (t) \cdot 1 + \sin (t) (- 1 \cos^{2} (t))$

Step 2.2

Factor $\sin (t)$ out of $\sin (t) \cdot 1 + \sin (t) (- 1 \cos^{2} (t))$ .

$\sin (t) \cdot (1 - 1 \cos^{2} (t))$

Step 2.3

Rewrite $- 1 \cos^{2} (t)$ as $- \cos^{2} (t)$ .

$\sin (t) \cdot (1 - \cos^{2} (t))$

Step 3

Apply pythagorean identity.

$\sin (t) \cdot \sin^{2} (t)$

Step 4

Multiply $\sin (t)$ by $\sin^{2} (t)$ by adding the exponents.

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Step 4.1

Multiply $\sin (t)$ by $\sin^{2} (t)$ .

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Step 4.1.1

Raise $\sin (t)$ to the power of $1$ .

$\sin^{1} (t) \cdot \sin^{2} (t)$

Step 4.1.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

${\sin (t)}^{1 + 2}$

Step 4.2

Add $1$ and $2$ .

$\sin^{3} (t)$