Question

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

Options

• x = 0

• y = 0

• x + y = 0

• x − y = 0

Answer 1

x + y = 0

\[\text { Given }: \]

\[y = \sin x\]

\[\text { On differentiating both sides w.r.t.x, we get }\]

\[\frac{dy}{dx} = \cos x\]

\[\text { Slope of the tangent }= \left( \frac{dy}{dx} \right)_\left( 0, 0 \right) = cos 0 =1\]

\[\text { Slope of the normal }, m=\frac{- 1}{1}=-1\]

\[\text { Given }: \]

\[\left( x_1 , y_1 \right) = \left( 0, 0 \right)\]

\[ \therefore \text { Equation of the normal }\]

\[ = y - y_1 = m\left( x - x_1 \right)\]

\[ \Rightarrow y - 0 = - 1\left( x - 0 \right)\]

\[ \Rightarrow y = - x\]

\[ \Rightarrow x + y = 0\]