Trigonometry Examples

$6 = \sqrt{144 - (12 \sin (x))}$

Step 1

Simplify $\sqrt{144 - (12 \sin (x))}$ .

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Step 1.1

Multiply $12$ by $- 1$ .

$6 = \sqrt{144 - 12 \sin (x)}$

Step 1.2

Factor $12$ out of $144 - 12 \sin (x)$ .

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Step 1.2.1

Factor $12$ out of $144$ .

$6 = \sqrt{12 (12) - 12 \sin (x)}$

Step 1.2.2

Factor $12$ out of $- 12 \sin (x)$ .

$6 = \sqrt{12 (12) + 12 (- \sin (x))}$

Step 1.2.3

Factor $12$ out of $12 (12) + 12 (- \sin (x))$ .

$6 = \sqrt{12 (12 - \sin (x))}$

Step 1.3

Rewrite $12 (12 - \sin (x))$ as $2^{2} \cdot (3 (12 - \sin (x)))$ .

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Step 1.3.1

Factor $4$ out of $12$ .

$6 = \sqrt{4 (3) (12 - \sin (x))}$

Step 1.3.2

Rewrite $4$ as $2^{2}$ .

$6 = \sqrt{2^{2} \cdot 3 (12 - \sin (x))}$

Step 1.3.3

Add parentheses.

$6 = \sqrt{2^{2} \cdot (3 (12 - \sin (x)))}$

Step 1.4

Pull terms out from under the radical.

$6 = 2 \sqrt{3 (12 - \sin (x))}$

Step 2

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

No solution

Step 3