  Find the points of horizontal tangency to the polar curve.r = a sin θ      0 ≤ θ < π, a > 0(r, θ) =     (smaller r value)(r, θ) =     (larger r value)Find the points of vertical tangency to the polar curve.(r, θ) =     (smaller θ value)(r, θ) =     (larger θ value)

Question

Find the points of horizontal tangency to the polar curve.

r = a sin θ      0 ≤ θ < π, a > 0
(r, θ) =

(smaller r value)

(r, θ) =

(larger r value)

Find the points of vertical tangency to the polar curve.

(r, θ) =

(smaller θ value)

(r, θ) =

(larger θ value)

Step 1

Calculation:

The polar curve is r = a sin θ, where 0 ≤ θ < π and a > 0.

In order to find the slope, convert to a parametric equation using x = r cos θ y = r sin θ.

Compute the slope using the above equation as follows.

Step 2

Further simplified as,

Step 3

Horizontal tangents occur whe...

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Calculus 