Trigonometry Examples

$(4 \sin^{2} (x) - 1) \sin (x) = 0$

Step 1

Simplify $(4 \sin^{2} (x) - 1) \sin (x)$ .

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Step 1.1

Apply the distributive property.

$4 \sin^{2} (x) \sin (x) - 1 \sin (x) = 0$

Step 1.2

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

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Step 1.2.1

Move $\sin (x)$ .

$4 (\sin (x) \sin^{2} (x)) - 1 \sin (x) = 0$

Step 1.2.2

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

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Step 1.2.2.1

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

$4 (\sin^{1} (x) \sin^{2} (x)) - 1 \sin (x) = 0$

Step 1.2.2.2

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

$4 {\sin (x)}^{1 + 2} - 1 \sin (x) = 0$

Step 1.2.3

Add $1$ and $2$ .

$4 \sin^{3} (x) - 1 \sin (x) = 0$

Step 1.3

Rewrite $- 1 \sin (x)$ as $- \sin (x)$ .

$4 \sin^{3} (x) - \sin (x) = 0$

Step 2

Graph each side of the equation. The solution is the x-value of the point of intersection.

$x = π n, \frac{π}{6} + π n, \frac{5 π}{6} + π n$ , for any integer $n$

Step 3