Trigonometry Examples

$120 = \frac{70^{2}}{16} \cdot (\cos (x) \sin (x))$

Step 1

Simplify $\frac{70^{2}}{16} \cdot (\cos (x) \sin (x))$ .

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Step 1.1

Raise $70$ to the power of $2$ .

$120 = \frac{4900}{16} \cdot (\cos (x) \sin (x))$

Step 1.2

Cancel the common factor of $4900$ and $16$ .

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Step 1.2.1

Factor $4$ out of $4900$ .

$120 = \frac{4 (1225)}{16} \cdot (\cos (x) \sin (x))$

Step 1.2.2

Cancel the common factors.

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Step 1.2.2.1

Factor $4$ out of $16$ .

$120 = \frac{4 \cdot 1225}{4 \cdot 4} \cdot (\cos (x) \sin (x))$

Step 1.2.2.2

Cancel the common factor.

$120 = \frac{4 \cdot 1225}{4 \cdot 4} \cdot (\cos (x) \sin (x))$

Step 1.2.2.3

Rewrite the expression.

$120 = \frac{1225}{4} \cdot (\cos (x) \sin (x))$

Step 1.3

Multiply $\frac{1225}{4} (\cos (x) \sin (x))$ .

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Step 1.3.1

Combine $\cos (x)$ and $\frac{1225}{4}$ .

$120 = \frac{\cos (x) \cdot 1225}{4} \sin (x)$

Step 1.3.2

Combine $\frac{\cos (x) \cdot 1225}{4}$ and $\sin (x)$ .

$120 = \frac{\cos (x) \cdot 1225 \sin (x)}{4}$

Step 1.4

Move $1225$ to the left of $\cos (x)$ .

$120 = \frac{1225 \cos (x) \sin (x)}{4}$

Step 2

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

$x \approx 0.45027885 + π n, 1.12051746 + π n$ , for any integer $n$

Step 3