Trigonometry Examples

$y = \sin (\frac{1}{3}) x$

Step 1

Rewrite the equation as $\sin (\frac{1}{3}) x = y$ .

$\sin (\frac{1}{3}) x = y$

Step 2

Divide each term in $\sin (\frac{1}{3}) x = y$ by $\sin (\frac{1}{3})$ and simplify.

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Step 2.1

Divide each term in $\sin (\frac{1}{3}) x = y$ by $\sin (\frac{1}{3})$ .

$\frac{\sin (\frac{1}{3}) x}{\sin (\frac{1}{3})} = \frac{y}{\sin (\frac{1}{3})}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $\sin (\frac{1}{3})$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{\sin (\frac{1}{3}) x}{\sin (\frac{1}{3})} = \frac{y}{\sin (\frac{1}{3})}$

Step 2.2.1.2

Divide $x$ by $1$ .

$x = \frac{y}{\sin (\frac{1}{3})}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Separate fractions.

$x = \frac{y}{1} \cdot \frac{1}{\sin (\frac{1}{3})}$

Step 2.3.2

Convert from $\frac{1}{\sin (\frac{1}{3})}$ to $\csc (\frac{1}{3})$ .

$x = \frac{y}{1} \csc (\frac{1}{3})$

Step 2.3.3

Divide $y$ by $1$ .

$x = y \csc (\frac{1}{3})$

Step 2.3.4

Evaluate $\csc (\frac{1}{3})$ .

$x = y \cdot 3.05628425$

Step 2.3.5

Move $3.05628425$ to the left of $y$ .

$x = 3.05628425 y$