Trigonometry Examples

$b = \sqrt{(56) \cdot 2} + (40) \cdot 2 - 2 \cdot 56 \cdot 40 \cos (22)$

Step 1

Simplify $\sqrt{(56) \cdot 2} + (40) \cdot 2 - 2 \cdot 56 \cdot 40 \cos (22)$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Multiply $56$ by $2$ .

$b = \sqrt{112} + (40) \cdot 2 - 2 \cdot 56 \cdot 40 \cos (22)$

Step 1.1.2

Rewrite $112$ as $4^{2} \cdot 7$ .

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Step 1.1.2.1

Factor $16$ out of $112$ .

$b = \sqrt{16 (7)} + (40) \cdot 2 - 2 \cdot 56 \cdot 40 \cos (22)$

Step 1.1.2.2

Rewrite $16$ as $4^{2}$ .

$b = \sqrt{4^{2} \cdot 7} + (40) \cdot 2 - 2 \cdot 56 \cdot 40 \cos (22)$

Step 1.1.3

Pull terms out from under the radical.

$b = 4 \sqrt{7} + (40) \cdot 2 - 2 \cdot 56 \cdot 40 \cos (22)$

Step 1.1.4

Multiply $40$ by $2$ .

$b = 4 \sqrt{7} + 80 - 2 \cdot 56 \cdot 40 \cos (22)$

Step 1.1.5

Multiply $- 2 \cdot 56 \cdot 40$ .

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Step 1.1.5.1

Multiply $- 2$ by $56$ .

$b = 4 \sqrt{7} + 80 - 112 \cdot 40 \cos (22)$

Step 1.1.5.2

Multiply $- 112$ by $40$ .

$b = 4 \sqrt{7} + 80 - 4480 \cos (22)$

Step 1.1.6

Evaluate $\cos (22)$ .

$b = 4 \sqrt{7} + 80 - 4480 \cdot 0.92718385$

Step 1.1.7

Multiply $- 4480$ by $0.92718385$ .

$b = 4 \sqrt{7} + 80 - 4153.78366845$

Step 1.2

Simplify by adding terms.

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Step 1.2.1

Subtract $4153.78366845$ from $4 \sqrt{7}$ .

$b = - 4143.20066321 + 80$

Step 1.2.2

Add $- 4143.20066321$ and $80$ .

$b = - 4063.20066321$

Step 2

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

No solution

Step 3