Trigonometry Examples

$y = \sin (x^{2})$

Step 1

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

$\sin (x^{2}) = y$

Step 2

Substitute $u$ for $x^{2}$ .

$\sin (u) = y$

Step 3

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

$u = \arcsin (y)$

Step 4

Substitute $x^{2}$ for $u$ and solve $x^{2} = \arcsin (y)$

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Step 4.1

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

$x = \pm \sqrt{\arcsin (y)}$

Step 4.2

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

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Step 4.2.1

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

$x = \sqrt{\arcsin (y)}$

Step 4.2.2

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

$x = - \sqrt{\arcsin (y)}$

Step 4.2.3

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

$x = \sqrt{\arcsin (y)}$

$x = - \sqrt{\arcsin (y)}$

$x = \sqrt{\arcsin (y)}$

$x = - \sqrt{\arcsin (y)}$

$x = \sqrt{\arcsin (y)}$

$x = - \sqrt{\arcsin (y)}$