Trigonometry Examples

$\sin (4 x) = 8 \cos^{3} (x) \sin (x - 4) \cos (x) \sin (x)$

Step 1

Multiply $\cos^{3} (x)$ by $\cos (x)$ by adding the exponents.

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Step 1.1

Move $\cos (x)$ .

$\sin (4 x) = 8 (\cos (x) \cos^{3} (x)) \sin (x - 4) \sin (x)$

Step 1.2

Multiply $\cos (x)$ by $\cos^{3} (x)$ .

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Step 1.2.1

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

$\sin (4 x) = 8 (\cos^{1} (x) \cos^{3} (x)) \sin (x - 4) \sin (x)$

Step 1.2.2

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

$\sin (4 x) = 8 {\cos (x)}^{1 + 3} \sin (x - 4) \sin (x)$

Step 1.3

Add $1$ and $3$ .

$\sin (4 x) = 8 \cos^{4} (x) \sin (x - 4) \sin (x)$

Step 2

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

$x \approx π n, 0.39399038 + π n, 0.73513435 + π n, \frac{π}{2} + π n$ , for any integer $n$

Step 3