Trigonometry Examples

$x = 1 + 2 \sin (t)$

Step 1

Rewrite the equation as $1 + 2 \sin (t) = x$ .

$1 + 2 \sin (t) = x$

Step 2

Subtract $1$ from both sides of the equation.

$2 \sin (t) = x - 1$

Step 3

Divide each term in $2 \sin (t) = x - 1$ by $2$ and simplify.

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Step 3.1

Divide each term in $2 \sin (t) = x - 1$ by $2$ .

$\frac{2 \sin (t)}{2} = \frac{x}{2} + \frac{- 1}{2}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $2$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{2 \sin (t)}{2} = \frac{x}{2} + \frac{- 1}{2}$

Step 3.2.1.2

Divide $\sin (t)$ by $1$ .

$\sin (t) = \frac{x}{2} + \frac{- 1}{2}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Move the negative in front of the fraction.

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

Step 4

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

$t = \arcsin (\frac{x}{2} - \frac{1}{2})$