Trigonometry Examples

x = t^{2}

$x = t^{2}$ ,

y = 2 t

$y = 2 t$

Step 1

Set up the parametric equation for

x (t)

$x (t)$ to solve the equation for

t

$t$ .

x = t^{2}

$x = t^{2}$

Step 2

Rewrite the equation as

t^{2} = x

$t^{2} = x$ .

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}

$t = \pm \sqrt{x}$

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

$\pm$ to find the first solution.

t = \sqrt{x}

$t = \sqrt{x}$

Step 4.2

Next, use the negative value of the

\pm

$\pm$ to find the second solution.

t = - \sqrt{x}

$t = - \sqrt{x}$

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}

$t = - \sqrt{x}$

t = \sqrt{x}

$t = \sqrt{x}$

t = - \sqrt{x}

$t = - \sqrt{x}$

Step 5

Replace

t

$t$ in the equation for

y

$y$ to get the equation in terms of

x

$x$ .

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

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

Step 6

Simplify

2 (\sqrt{x}, - \sqrt{x})

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

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Step 6.1

Multiply

2

$2$ by each element of the matrix.

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

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

Step 6.2

Multiply

- 1

$- 1$ by

2

$2$ .

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

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

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

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