Find the slope of the tangent line to the polar curve at the given point.
A) 0
B) 1
D) undefined

Question

Find the slope of the tangent line to the polar curve at the given point. 
A) 0 
B) 1 
D) undefined

Quizplus · Accepted Answer

To find the slope of the tangent line to a polar curve at a given point, we use the formula:
slope = dy/dx = (dy/dθ)/(dx/dθ) = (r' sinθ + r cosθ)/(r' cosθ - r sinθ)
where r is the distance from the origin to the point on the curve, and r' is the derivative of r with respect to θ.
At the given point, the curve is not specified, so we do not know r or r'. However, we do know that the tangent line is vertical (i.e. has an undefined slope) when the polar curve has a vertical tangent. This occurs when r' = 0 or when the curve is a circle with center at the origin. Therefore, the answer is D (undefined).

Find the Slope of the Tangent Line to the Polar