Trigonometry Examples

$\sqrt{72 - 72 \cos (x)}$

Step 1

Factor $72$ out of $72 - 72 \cos (x)$ .

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Step 1.1

Factor $72$ out of $72$ .

$\sqrt{72 (1) - 72 \cos (x)}$

Step 1.2

Factor $72$ out of $- 72 \cos (x)$ .

$\sqrt{72 (1) + 72 (- \cos (x))}$

Step 1.3

Factor $72$ out of $72 (1) + 72 (- \cos (x))$ .

$\sqrt{72 (1 - \cos (x))}$

Step 2

Rewrite $72 (1 - \cos (x))$ as $6^{2} \cdot (2 (1^{2} - \cos (x)))$ .

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Step 2.1

Factor $36$ out of $72$ .

$\sqrt{36 (2) (1 - \cos (x))}$

Step 2.2

Rewrite $36$ as $6^{2}$ .

$\sqrt{6^{2} \cdot 2 (1 - \cos (x))}$

Step 2.3

Rewrite $1$ as $1^{2}$ .

$\sqrt{6^{2} \cdot 2 (1^{2} - \cos (x))}$

Step 2.4

Add parentheses.

$\sqrt{6^{2} \cdot (2 (1^{2} - \cos (x)))}$

Step 3

Pull terms out from under the radical.

$6 \sqrt{2 (1^{2} - \cos (x))}$

Step 4

One to any power is one.

$6 \sqrt{2 (1 - \cos (x))}$