Question

$\huge\mathcal{\underline{QUESTION :}}$
Write the parametric equations below in Cartesian coordinates. x = 3 cos(t); y = 4 sin(t).
$\large\mathcal{\underline{Only \: for \: stars \: and \: mods}}$​

Answer 1

$\large\bf\underline{Given:-}$

• x = 3 cos(t).
• y = 4 sin(t).

$\huge\bf\underline{Solution:-}$

We can write first equation as :

$x = 3 \cos(t) \implies \cos(t) = \frac{x}{3} \implies \: t = { \cos}^{ - 1} ( \frac{x}{3} )$

Next, isolate t from the second equation:

$y = 4 \sin(t) \implies \sin(t) = \frac{y}{4} \implies \: t = { \sin}^{ - 1} ( \frac{y}{4} )$

Now, equating both values of t.

$\implies { \cos}^{ - 1} ( \frac{x}{3} ) = { \sin}^{ - 1} ( \frac{y}{4} ) \\ \implies \frac{x}{3} = \cos(arcsin( \frac{y}{4} ) ) \\ \implies \: x = 3\cos(arcsin( \frac{y}{4} ) )$

Therefore, the Cartesian equation of the curve is x = $3\cos(arcsin( \frac{y}{4} ) )$

Answer 2

Step-by-step explanation:

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