If the parameter $t$ of $x$ and $y$ in a plane is given in the interval $(- ∞ , ∞)$ and if $x = t cos (t)$ and $y = t sin (t)$ How can one eliminate the parameter t and write a single equation using only $y$ and $x$?
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Hint:
Do we know something about $\sin^2 \theta + \cos^2 \theta$?
And how can we obtain that from the parametric equations given?
EDIT(Response to Q in comments):
Dividing the equations will help you eliminate the resulting $t$ in the last step.
Vizag
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1Formatting hint: if you prefix the trigonometric functions' names with a backslash, LaTeX/MathJax will know they are functions' symbols and render them in upright font with appriopriate spacing:
t\sin x→ $t\sin x$, instead of a formless mass of italics:t sin x→ $t sin x$. – CiaPan Apr 29 '19 at 10:53 -
Divide the 2 equations. $tan(t) = \frac{y}{x}$. Therefore $t= tan^{-1}(y/x)$. Substitute that in the above equation obtained. – Vizag Apr 29 '19 at 10:54
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t\sin x→ $t\sin x$, instead of a formless mass of italics:t sin x→ $t sin x$. – CiaPan Apr 29 '19 at 10:56