Trigonometry Examples

${6.2}^{2} = {6.7}^{2} + {6.1}^{2} - 2 \cdot 6.7 \cdot 6.1 \cdot \cos (x)$

Step 1

Raise $6.2$ to the power of $2$ .

$38.44 = {6.7}^{2} + {6.1}^{2} - 2 \cdot 6.7 \cdot 6.1 \cdot \cos (x)$

Step 2

Simplify ${6.7}^{2} + {6.1}^{2} - 2 \cdot 6.7 \cdot 6.1 \cdot \cos (x)$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Raise $6.7$ to the power of $2$ .

$38.44 = 44.89 + {6.1}^{2} - 2 \cdot 6.7 \cdot 6.1 \cdot \cos (x)$

Step 2.1.2

Raise $6.1$ to the power of $2$ .

$38.44 = 44.89 + 37.21 - 2 \cdot 6.7 \cdot 6.1 \cdot \cos (x)$

Step 2.1.3

Multiply $- 2 \cdot 6.7 \cdot 6.1$ .

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Step 2.1.3.1

Multiply $- 2$ by $6.7$ .

$38.44 = 44.89 + 37.21 - 13.4 \cdot 6.1 \cdot \cos (x)$

Step 2.1.3.2

Multiply $- 13.4$ by $6.1$ .

$38.44 = 44.89 + 37.21 - 81.74 \cdot \cos (x)$

$38.44 = 44.89 + 37.21 - 81.74 \cos (x)$

Step 2.2

Add $44.89$ and $37.21$ .

$38.44 = 82.1 - 81.74 \cos (x)$

Step 3

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

$x \approx 1.00731491 + 2 π n, 5.27587039 + 2 π n$ , for any integer $n$

Step 4