The slope of the line tangent to the polar curve r = 3θ at the point where θ = π/2 is; Undefined
By converting into parametric equations, we have;
x(θ) = r(θ) cos θ = cos 3θ cos θ
y(θ) = r(θ) sin θ = cos 3θ sin θ
By product rule;
x'(θ) = -sin 3θ cos θ - cos 3θ sin θ
x'(π/2) = -sin 3(π/2) cos (π/2) - cos 3(π/2) sin (π/2)
x'(π/2) = 0
y'(θ) = -sin 3θ sin θ + cos 3θ cos θ
y'(π/2) = -sin 3(π/2) sin (π/2) + cos 3(π/2) cos (π/2)
y'(π/2) = 1
The slope m of the curve is gotten from;
m = y'(π/2)/x'(π/2)
m = 1/0
Thus the slope is undefined
Read more about slope of line tangent at; https://brainly.com/question/6353432
