Trigonometry Examples

$14^{2} = 11^{2} + 15^{2} - 2 \cdot 15 \cdot 11 \cdot \cos (x)$

Step 1

Raise $14$ to the power of $2$ .

$196 = 11^{2} + 15^{2} - 2 \cdot 15 \cdot 11 \cdot \cos (x)$

Step 2

Simplify $11^{2} + 15^{2} - 2 \cdot 15 \cdot 11 \cdot \cos (x)$ .

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Simplify each term.

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Raise $11$ to the power of $2$ .

$196 = 121 + 15^{2} - 2 \cdot 15 \cdot 11 \cdot \cos (x)$

Raise $15$ to the power of $2$ .

$196 = 121 + 225 - 2 \cdot 15 \cdot 11 \cdot \cos (x)$

Multiply $- 2 \cdot 15 \cdot 11$ .

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Multiply $- 2$ by $15$ .

$196 = 121 + 225 - 30 \cdot 11 \cdot \cos (x)$

Multiply $- 30$ by $11$ .

$196 = 121 + 225 - 330 \cdot \cos (x)$

$196 = 121 + 225 - 330 \cos (x)$

Add $121$ and $225$ .

$196 = 346 - 330 \cos (x)$

Step 3

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

$x \approx 1.09893448 + 2 π n, 5.18425081 + 2 π n$ , for any integer $n$

Step 4