Question

If y = cos t and x = sin t, then what is $\frac{dy}{dx}$ equal to ?

• A. $xy$
• B. $\frac{x}{y}$
• C. $-\frac{y}{x}$
• D. $-\frac{x}{y}$

Answer 1

Answer: (D)

$-\frac{x}{y}$

Differentiating $x,y$ wrt $t,$ we get

$\frac{dx}{dt}=\frac{d}{dt}\left(\cos t\right)=-\sin t$ and

$\frac{dx}{dt}=\frac{d}{dt}\left(\sin t\right)=\cos t$

$\therefore \frac{dy}{dx}=\frac{\left(\frac{dy}{dt}\right)}{\left(\frac{dx}{dt}\right)}=\frac{-\sin t}{\cos t}=-\frac{x}{y}$