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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