Trigonometry Examples

y = sin (\frac{1}{2}) (x - c)

$y = \sin (\frac{1}{2}) (x - c)$

Step 1

Rewrite the equation as

sin (\frac{1}{2}) (x - c) = y

$\sin (\frac{1}{2}) (x - c) = y$ .

sin (\frac{1}{2}) (x - c) = y

$\sin (\frac{1}{2}) (x - c) = y$

Step 2

Divide each term in

sin (\frac{1}{2}) (x - c) = y

$\sin (\frac{1}{2}) (x - c) = y$ by

sin (\frac{1}{2})

$\sin (\frac{1}{2})$ and simplify.

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Step 2.1

Divide each term in

sin (\frac{1}{2}) (x - c) = y

$\sin (\frac{1}{2}) (x - c) = y$ by

sin (\frac{1}{2})

$\sin (\frac{1}{2})$ .

\frac{sin (\frac{1}{2}) (x - c)}{sin (\frac{1}{2})} = \frac{y}{sin (\frac{1}{2})}

$\frac{\sin (\frac{1}{2}) (x - c)}{\sin (\frac{1}{2})} = \frac{y}{\sin (\frac{1}{2})}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of

sin (\frac{1}{2})

$\sin (\frac{1}{2})$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{\sin (\frac{1}{2}) (x - c)}{\sin (\frac{1}{2})} = \frac{y}{\sin (\frac{1}{2})}$

Step 2.2.1.2

Divide

$x - c$ by

$1$ .

$x - c = \frac{y}{\sin (\frac{1}{2})}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Separate fractions.

$x - c = \frac{y}{1} \cdot \frac{1}{\sin (\frac{1}{2})}$

Step 2.3.2

Convert from

$\frac{1}{\sin (\frac{1}{2})}$ to

$\csc (\frac{1}{2})$ .

$x - c = \frac{y}{1} \csc (\frac{1}{2})$

Step 2.3.3

Divide

$y$ by

$1$ .

$x - c = y \csc (\frac{1}{2})$

Step 2.3.4

Evaluate

$\csc (\frac{1}{2})$ .

$x - c = y \cdot 2.08582964$

Step 2.3.5

Move

$2.08582964$ to the left of

$y$ .

$x - c = 2.08582964 y$

Step 3

Subtract

$x$ from both sides of the equation.

$- c = 2.08582964 y - x$

Step 4

Divide each term in

$- c = 2.08582964 y - x$ by

$- 1$ and simplify.

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Step 4.1

Divide each term in

$- c = 2.08582964 y - x$ by

$- 1$ .

$\frac{- c}{- 1} = \frac{2.08582964 y}{- 1} + \frac{- x}{- 1}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Dividing two negative values results in a positive value.

$\frac{c}{1} = \frac{2.08582964 y}{- 1} + \frac{- x}{- 1}$

Step 4.2.2

Divide

$c$ by

$1$ .

$c = \frac{2.08582964 y}{- 1} + \frac{- x}{- 1}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Simplify each term.

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Step 4.3.1.1

Move the negative one from the denominator of

$\frac{2.08582964 y}{- 1}$ .

$c = - 1 \cdot (2.08582964 y) + \frac{- x}{- 1}$

Step 4.3.1.2

Rewrite

$- 1 \cdot (2.08582964 y)$ as

$- (2.08582964 y)$ .

$c = - (2.08582964 y) + \frac{- x}{- 1}$

Step 4.3.1.3

Multiply

$2.08582964$ by

$- 1$ .

$c = - 2.08582964 y + \frac{- x}{- 1}$

Step 4.3.1.4

Dividing two negative values results in a positive value.

$c = - 2.08582964 y + \frac{x}{1}$

Step 4.3.1.5

Divide

$x$ by

$1$ .

$c = - 2.08582964 y + x$