Trigonometry Examples

$b^{2} = {13.7}^{2} + 20.1 - 2 \cdot 13.7 (20.1 \cos (66.5))$

Step 1

Move all the expressions to the left side of the equation.

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Step 1.1

Subtract ${13.7}^{2}$ from both sides of the equation.

$b^{2} - {13.7}^{2} = 20.1 - 2 \cdot 13.7 (20.1 \cos (66.5))$

Step 1.2

Subtract $20.1$ from both sides of the equation.

$b^{2} - {13.7}^{2} - 20.1 = - 2 \cdot 13.7 (20.1 \cos (66.5))$

Step 1.3

Add $2 \cdot 13.7 (20.1 \cos (66.5))$ to both sides of the equation.

$b^{2} - {13.7}^{2} - 20.1 + 2 \cdot 13.7 (20.1 \cos (66.5)) = 0$

Step 2

Simplify $b^{2} - {13.7}^{2} - 20.1 + 2 \cdot 13.7 (20.1 \cos (66.5))$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Raise $13.7$ to the power of $2$ .

$b^{2} - 1 \cdot 187.69 - 20.1 + 2 \cdot 13.7 (20.1 \cos (66.5)) = 0$

Step 2.1.2

Multiply $- 1$ by $187.69$ .

$b^{2} - 187.69 - 20.1 + 2 \cdot 13.7 (20.1 \cos (66.5)) = 0$

Step 2.1.3

Multiply $2$ by $13.7$ .

$b^{2} - 187.69 - 20.1 + 27.4 (20.1 \cos (66.5)) = 0$

Step 2.1.4

Multiply $20.1$ by $\cos (66.5)$ .

$b^{2} - 187.69 - 20.1 + 27.4 \cdot 8.01485628 = 0$

Step 2.1.5

Multiply $27.4$ by $8.01485628$ .

$b^{2} - 187.69 - 20.1 + 219.60706221 = 0$

Step 2.2

Subtract $20.1$ from $- 187.69$ .

$b^{2} - 207.79 + 219.60706221 = 0$

Step 2.3

Add $- 207.79$ and $219.60706221$ .

$b^{2} + 11.81706221 = 0$

Step 3

The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.