Question

Find the slope of the tangent line to the given polar curve at

the point specified by the value of theta. r = 8 cos(theta), theta = ( /3)

Answer 1

The slope of the tangent line to the polar curve r = 8 cos(theta) at theta = pi/3 is -4√3.

Step-by-step explanation:

The slope of the tangent line to a polar curve can be found by taking the derivative of the polar curve equation with respect to theta.

Given that r = 8 cos(theta), we can differentiate this equation to find the derivative: dr/dtheta = -8 sin(theta).

At theta = pi/3, the slope of the tangent line is dr/dtheta = -8 sin(pi/3) = -8(√3/2) = -4√3.