Trigonometry Examples

${| v |}^{2} = 48^{2} + 60^{2} - 2 \cdot 48 \cdot 60 \cos (130)$

Step 1

Remove the absolute value in ${| v |}^{2}$ because exponentiations with even powers are always positive.

$v^{2} = 48^{2} + 60^{2} - 2 \cdot 48 \cdot 60 \cos (130)$

Step 2

Simplify $48^{2} + 60^{2} - 2 \cdot 48 \cdot 60 \cos (130)$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Raise $48$ to the power of $2$ .

$v^{2} = 2304 + 60^{2} - 2 \cdot 48 \cdot 60 \cos (130)$

Step 2.1.2

Raise $60$ to the power of $2$ .

$v^{2} = 2304 + 3600 - 2 \cdot 48 \cdot 60 \cos (130)$

Step 2.1.3

Multiply $- 2 \cdot 48 \cdot 60$ .

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Step 2.1.3.1

Multiply $- 2$ by $48$ .

$v^{2} = 2304 + 3600 - 96 \cdot 60 \cos (130)$

Step 2.1.3.2

Multiply $- 96$ by $60$ .

$v^{2} = 2304 + 3600 - 5760 \cos (130)$

Step 2.1.4

Evaluate $\cos (130)$ .

$v^{2} = 2304 + 3600 - 5760 \cdot - 0.6427876$

Step 2.1.5

Multiply $- 5760$ by $- 0.6427876$ .

$v^{2} = 2304 + 3600 + 3702.45663179$

Step 2.2

Simplify by adding numbers.

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Step 2.2.1

Add $2304$ and $3600$ .

$v^{2} = 5904 + 3702.45663179$

Step 2.2.2

Add $5904$ and $3702.45663179$ .

$v^{2} = 9606.45663179$

Step 3

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

No solution

Step 4