What is the implicit form of $x=cos(t),y=-3+cos(2t)$?

Question

I know I have to use the properties of the trigonometric functions but I don't know which of them would help me get the answer.

What is the implicit form for that parametric equation? – Nicolás Siplis Jul 17 '15 at 00:54 — Nicolás Siplis, Jul 17 '15 at 00:54

score 3 · Accepted Answer · answered Jul 17 '15 at 00:55

3

$y + 3 = \cos (2t) = 2\cos^2t-1 = 2x^2-1\to y = 2x^2-4$. So if you want to find $\dfrac{dy}{dx}$ then from this $y' = 4x$

answered Jul 17 '15 at 00:55

DeepSea

score 1 · Answer 2 · answered Jul 17 '15 at 00:55

1

Hint: Use chain rule: $\frac{dy}{dx}=\frac{dy}{dt} \times \frac{dt}{dx}$. First find $\frac{dy}{dt}$ and $\frac{dx}{dt}$.

answered Jul 17 '15 at 00:55

Chuks

2 Answers2