STEM Lessons for College Students

Polar Coordinates: Example 9: Cardioid: Part 2: Question A

In this video I go over Part 2 of Example 9 on Polar Coordinates, and this time continue on solving Question A of that Example. From Part 1 I derived the formula for slope of the tangent line dy/dx for the Cardioid r = 1 + sinϴ. In this Part 2, I use that derived formula to solve for the slope of the line tangent to the point on the Cardioid curve where ϴ = π/3. The slope turns out to be -1, and this can be visually seen by sketching a line tangent to the Cardioid. I also use a good trick to remember exact trigonometric ratios for the angle π/3, which is drawing an isosceles triangle with sides of equal length 2. From here we can easily derive the ratios for sin(π/3) and cos(π/3), which we can then plug into the dy/dx formula. This is a quick, yet very useful video in determining the slopes of tangents lines to polar curves, so make sure to watch this video!

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