The equation to the normal to the curve y = sin x at (0, 0) is ___________ .

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x + y = 0 \text { Given }: y = \sin x \text { On differentiating both sides w.r.t.x, we get } dy/dx = \cos x \text { Slope of the tangent }= \left( dy/dx \right)_\left( 0, 0 \right) = cos 0 =1 \text { Slope of the normal }, m=- $\frac{1}{1}$=-1 \text { Given }: \left( x_1 , y_1 \right) = \left( 0, 0 \right) \therefore \text { Equation of the normal } = y - y_1 = m\left( x - x_1 \right) \Rightarrow y - 0 = - 1\left( x - 0 \right) \Rightarrow y = - x \Rightarrow x + y = 0

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