What is the equation of the tangent to the curve y = sin x at (0, 0)?1

1.	What is the equation of the tangent to the curve y = sin x at (0, 0)?1. x + y = 02. x - y = 03. 2x + y = 04. 2x - y = 0
Answer» Correct Answer - Option 2 : x - y = 0 Concept: Steps to find the equation of the tangent to the curve: 1) Find the first derivative of f(x). 2) Use the point-slope formula to find the equation for the tangent line. Point-slope is the general form: y - y₁=m(x - x₁), Where m = slope of tangent = \(\rm \frac {dy}{dx}\) Calculation: Here, y = sin x \(\rm \frac {dy}{dx}\) = cos x \(\rm \frac{dy}{dx}\|_{x=0}\)= cos 0 = 1 So, Slope = 1 So, Equation of tangent to the curve is (y - 0) = 1(x - 0) ⇒ y = x ⇒ x - y = 0 Hence, option (2) is correct.

What is the equation of the tangent to the curve y = sin x at (0, 0)?1. x + y = 02. x - y = 03. 2x + y = 04. 2x - y = 0

Answer» Correct Answer - Option 2 : x - y = 0

Concept:

Steps to find the equation of the tangent to the curve:

1) Find the first derivative of f(x).

2) Use the point-slope formula to find the equation for the tangent line.

Point-slope is the general form:

y - y₁=m(x - x₁), Where m = slope of tangent = \(\rm \frac {dy}{dx}\)

Calculation:

Here, y = sin x

\(\rm \frac {dy}{dx}\) = cos x

\(\rm \frac{dy}{dx}|_{x=0}\)= cos 0 = 1

So, Slope = 1

So, Equation of tangent to the curve is (y - 0) = 1(x - 0)

⇒ y = x

⇒ x - y = 0

Hence, option (2) is correct.

Discussion

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