Find the equation of the line tangent to the graph of y = sin x at the point where x = 0.
A) y = cos x
B) y = x
C) y = -x

Question

Quizplus · Accepted Answer

The derivative of y = sin x is y' = cos x. When x = 0, y' = cos 0 = 1. So the slope of the tangent line at x = 0 is 1. The point (0, sin 0) is just (0,0). Using the point-slope form of the equation of a line, the equation of the tangent line is y - 0 = 1(x - 0), which simplifies to y = x. Therefore, the correct answer is B.

Find the Equation of the Line Tangent to the Graph