Question

For the curve r = 5sinθ, find the slope of the tangent line when θ = π / 2.

Answer 1

we know that a derivative in polar co ordinate is given by,

    --------------------------------------------------1)

which is nothing but the slope of tangent line

we have,

Hence,

Put this value in equation 1) we have,

we have,

Hence,

we know that,

Hence we can say that,

we know that,

Hence,

we have to find the slope at theta = pi/2 which is given by,

Hence we can say that slope of the tangent line to the curve r = 5sin(theta) when theta = pi/2 is 0