# implicit differentiation, tangent line help

#### Tweety

Find the equation to the tangent and the normal to the curve $$\displaystyle sinx siny = \frac{\sqrt{3}}{4}$$

at the point ( $$\displaystyle \frac{\pi}{3} , \frac{\pi}{6}$$ )

I keep getting this question wrong, here's my working;

using the product rule on sinxsiny
$$\displaystyle sinx cosy \frac{dy}{dx} + siny cosx = 0$$

$$\displaystyle \frac{dy}{dx} = -\frac{ siny cosx}{sinx cosy}$$

Is this part correct?

#### tonio

Find the equation to the tangent and the normal to the curve $$\displaystyle sinx siny = \frac{\sqrt{3}}{4}$$

at the point ( $$\displaystyle \frac{\pi}{3} , \frac{\pi}{6}$$ )

I keep getting this question wrong, here's my working;

using the product rule on sinxsiny
$$\displaystyle sinx cosy \frac{dy}{dx} + siny cosx = 0$$

$$\displaystyle \frac{dy}{dx} = -\frac{ siny cosx}{sinx cosy}$$

Is this part correct?

Yes, it is. Now just note that $$\displaystyle \frac{\cos x\sin y}{\sin x\cos y}=-\frac{\tan y}{\tan x}$$ ...

Tonio

HallsofIvy