Trigonometry Examples

$x = t^{2}$ , $y = 2 t$

Step 1

Set up the parametric equation for $x (t)$ to solve the equation for $t$ .

$x = t^{2}$

Step 2

Rewrite the equation as $t^{2} = x$ .

$t^{2} = x$

Step 3

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

$t = \pm \sqrt{x}$

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.

$t = \sqrt{x}$

Step 4.2

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

$t = - \sqrt{x}$

Step 4.3

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

$t = \sqrt{x}$

$t = - \sqrt{x}$

$t = \sqrt{x}$

$t = - \sqrt{x}$

Step 5

Replace $t$ in the equation for $y$ to get the equation in terms of $x$ .

$y = 2 (\sqrt{x}, - \sqrt{x})$

Step 6

Simplify $2 (\sqrt{x}, - \sqrt{x})$ .

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Step 6.1

Multiply $2$ by each element of the matrix.

$y = (2 \sqrt{x}, 2 (- \sqrt{x}))$

Step 6.2

Multiply $- 1$ by $2$ .

$y = (2 \sqrt{x}, - 2 \sqrt{x})$