truly parametric

Calculus Level 1

if y = cos ⁡ 2 t y= \cos{2t} and x = sin ⁡ t x= \sin{t} .

Find the expression for d y d x \frac{dy}{dx} .

1) 2 sin ⁡ t 2\sin{t}

2) − 4 sin ⁡ t -4\sin{t}

3) − 4 sin ⁡ 2 t -4\sin{2t}

4) − 2 sin ⁡ 2 t -2\sin{2t} type your answer as 1 or 2 or 3 or 4 in the answer box


The answer is 2.

Samuel Ayinde by samuel ayinde , 24, Nigeria

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1 solution

We have , y = c o s ( 2 t ) and x = s i n ( t ) y = cos(2t) \text{ and } x = sin(t) Now differentiating both equations we get, d y d t = − 2 s i n ( 2 t ) → ( i ) \frac{dy}{dt} = -2sin(2t) \rightarrow(i) and, d x d t = c o s t → ( i i ) \frac{dx}{dt} = cost \rightarrow(ii) ( i ) / ( i i ) (i)/(ii) gives, d y d x = − 2 × s i n ( 2 t ) c o s ( t ) ⇒ − 2 × 2 × s i n t × c o s t c o s t ⇒ − 4 s i n t \frac{dy}{dx} = \dfrac{-2 \times sin(2t)}{cos(t)} \Rightarrow \dfrac{-2\times 2\times sint\times cost}{cost} \Rightarrow \boxed{-4sint}

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