Trigonometry Examples

$y = 3 \sin (x - \frac{π}{2})$

Step 1

Rewrite the equation as $3 \sin (x - \frac{π}{2}) = y$ .

$3 \sin (x - \frac{π}{2}) = y$

Step 2

Divide each term in $3 \sin (x - \frac{π}{2}) = y$ by $3$ and simplify.

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Step 2.1

Divide each term in $3 \sin (x - \frac{π}{2}) = y$ by $3$ .

$\frac{3 \sin (x - \frac{π}{2})}{3} = \frac{y}{3}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $3$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{3 \sin (x - \frac{π}{2})}{3} = \frac{y}{3}$

Step 2.2.1.2

Divide $\sin (x - \frac{π}{2})$ by $1$ .

$\sin (x - \frac{π}{2}) = \frac{y}{3}$

Step 3

Take the inverse sine of both sides of the equation to extract $x$ from inside the sine.

$x - \frac{π}{2} = \arcsin (\frac{y}{3})$

Step 4

Add $\frac{π}{2}$ to both sides of the equation.

$x = \arcsin (\frac{y}{3}) + \frac{π}{2}$