Trigonometry Examples

$5 \sin (x) \cos^{2} (x) = 5 \sin (x)$

Step 1

Subtract $5 \sin (x)$ from both sides of the equation.

$5 \sin (x) \cos^{2} (x) - 5 \sin (x) = 0$

Step 2

Simplify $5 \sin (x) \cos^{2} (x) - 5 \sin (x)$ .

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Step 2.1

Reorder $5 \sin (x) \cos^{2} (x)$ and $- 5 \sin (x)$ .

$- 5 \sin (x) + 5 \sin (x) \cos^{2} (x) = 0$

Step 2.2

Factor $- 5 \sin (x)$ out of $- 5 \sin (x)$ .

$- 5 \sin (x) (1) + 5 \sin (x) \cos^{2} (x) = 0$

Step 2.3

Factor $- 5 \sin (x)$ out of $5 \sin (x) \cos^{2} (x)$ .

$- 5 \sin (x) (1) - 5 \sin (x) (- 1 \cos^{2} (x)) = 0$

Step 2.4

Factor $- 5 \sin (x)$ out of $- 5 \sin (x) (1) - 5 \sin (x) (- 1 \cos^{2} (x))$ .

$- 5 \sin (x) (1 - 1 \cos^{2} (x)) = 0$

Step 2.5

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

$- 5 \sin (x) (1 - \cos^{2} (x)) = 0$

Step 2.6

Apply pythagorean identity.

$- 5 \sin (x) \sin^{2} (x) = 0$

Step 2.7

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

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Step 2.7.1

Move $\sin^{2} (x)$ .

$- 5 (\sin^{2} (x) \sin (x)) = 0$

Step 2.7.2

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

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Step 2.7.2.1

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

$- 5 (\sin^{2} (x) \sin^{1} (x)) = 0$

Step 2.7.2.2

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

$- 5 {\sin (x)}^{2 + 1} = 0$

Step 2.7.3

Add $2$ and $1$ .

$- 5 \sin^{3} (x) = 0$

Step 3

The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.