Trigonometry Examples

x = t^{2} + 3

$x = t^{2} + 3$ ,

y = 4 t

$y = 4 t$

Step 1

Set up the parametric equation for

x (t)

$x (t)$ to solve the equation for

t

$t$ .

x = t^{2} + 3

$x = t^{2} + 3$

Step 2

Rewrite the equation as

t^{2} + 3 = x

$t^{2} + 3 = x$ .

t^{2} + 3 = x

$t^{2} + 3 = x$

Step 3

Subtract

3

$3$ from both sides of the equation.

t^{2} = x - 3

$t^{2} = x - 3$

Step 4

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

t = \pm \sqrt{x - 3}

$t = \pm \sqrt{x - 3}$

Step 5

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

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Step 5.1

First, use the positive value of the

\pm

$\pm$ to find the first solution.

t = \sqrt{x - 3}

$t = \sqrt{x - 3}$

Step 5.2

Next, use the negative value of the

\pm

$\pm$ to find the second solution.

t = - \sqrt{x - 3}

$t = - \sqrt{x - 3}$

Step 5.3

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

t = \sqrt{x - 3}

$t = \sqrt{x - 3}$

t = - \sqrt{x - 3}

$t = - \sqrt{x - 3}$

t = \sqrt{x - 3}

$t = \sqrt{x - 3}$

t = - \sqrt{x - 3}

$t = - \sqrt{x - 3}$

Step 6

Replace

t

$t$ in the equation for

y

$y$ to get the equation in terms of

x

$x$ .

y = 4 (\sqrt{x - 3}, - \sqrt{x - 3})

$y = 4 (\sqrt{x - 3}, - \sqrt{x - 3})$

Step 7

Simplify

4 (\sqrt{x - 3}, - \sqrt{x - 3})

$4 (\sqrt{x - 3}, - \sqrt{x - 3})$ .

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Step 7.1

Multiply

4

$4$ by each element of the matrix.

y = (4 \sqrt{x - 3}, 4 (- \sqrt{x - 3}))

$y = (4 \sqrt{x - 3}, 4 (- \sqrt{x - 3}))$

Step 7.2

Multiply

- 1

$- 1$ by

4

$4$ .

y = (4 \sqrt{x - 3}, - 4 \sqrt{x - 3})

$y = (4 \sqrt{x - 3}, - 4 \sqrt{x - 3})$

y = (4 \sqrt{x - 3}, - 4 \sqrt{x - 3})

$y = (4 \sqrt{x - 3}, - 4 \sqrt{x - 3})$