Calculus Examples

$f (1.2) = \sin^{2} (x)$

Step 1

Rewrite the equation as $\sin^{2} (x) = f (1.2)$ .

$\sin^{2} (x) = f (1.2)$

Step 2

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$\sin (x) = \pm \sqrt{f (1.2)}$

Step 3

Simplify $\pm \sqrt{f (1.2)}$ .

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Step 3.1

Rewrite $f (1.2)$ as ${({1.04663513}^{2})}^{2} \cdot f$ .

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Step 3.1.1

Rewrite $1.2$ as ${1.09544511}^{2}$ .

$\sin (x) = \pm \sqrt{f \cdot {1.09544511}^{2}}$

Step 3.1.2

Reorder $f$ and ${1.09544511}^{2}$ .

$\sin (x) = \pm \sqrt{{1.09544511}^{2} \cdot f}$

Step 3.1.3

Rewrite $1.09544511$ as ${1.04663513}^{2}$ .

$\sin (x) = \pm \sqrt{{({1.04663513}^{2})}^{2} \cdot f}$

Step 3.2

Pull terms out from under the radical.

$\sin (x) = \pm {1.04663513}^{2} \sqrt{f}$

Step 3.3

Raise $1.04663513$ to the power of $2$ .

$\sin (x) = \pm 1.09544511 \sqrt{f}$

Step 4

The complete solution is the result of both the positive and negative portions of the solution.

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Step 4.1

First, use the positive value of the $\pm$ to find the first solution.

$\sin (x) = 1.09544511 \sqrt{f}$

Step 4.2

Next, use the negative value of the $\pm$ to find the second solution.

$\sin (x) = - 1.09544511 \sqrt{f}$

Step 4.3

The complete solution is the result of both the positive and negative portions of the solution.

$\sin (x) = 1.09544511 \sqrt{f}, - 1.09544511 \sqrt{f}$

Step 5

Set up each of the solutions to solve for $x$ .

$\sin (x) = 1.09544511 \sqrt{f}$

$\sin (x) = - 1.09544511 \sqrt{f}$

Step 6

Solve for $x$ in $\sin (x) = 1.09544511 \sqrt{f}$ .

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Step 6.1

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

$x = \arcsin (1.09544511 \sqrt{f})$

Step 7

Solve for $x$ in $\sin (x) = - 1.09544511 \sqrt{f}$ .

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Step 7.1

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

$x = \arcsin (- 1.09544511 \sqrt{f})$

Step 8

List all of the solutions.

$x = \arcsin (1.09544511 \sqrt{f})$

$x = \arcsin (- 1.09544511 \sqrt{f})$