Did you know that writing the equation of tangents to polar curves is surprisingly similar to writing equations of lines tangent in rectangular coordinates?
Yep! You still need a point and a slope!
The problem is that in order to write an equation you need an everything in terms of x and y, but the polar curve is in terms of r and theta.
Not to worry! There is a simply formula for finding the slope of tangent lines in polar that automatically converts in terms of x and y.
Formula for Slope of Polar Curve
And, to find the point, we just use our handy-dandy conversions we learned in the lesson regarding polar coordinates, and we have everything we need!
Simple!
So first, we’ll explore the difference between finding the derivative of a polar function and finding the slope of the tangent line.
Then we’ll investigate how to derive the slope of a tangent line in polar, which as Paul’s Online Notes nicely points out is very similar to how we find the slopes of parametric curves as well.
Next, you’ll learn how to find horizontal and vertical tangents with respect to polar curves. Which is nothing more than taking our derivative formula and either setting the numerator equal to zero the denominator equal to zero.
Additionally, we will draw upon our previous knowledge of derivatives and our First Derivative Test for finding extrema (i.e., maximums and minimums) throughout this lesson.
Tangent Line in Polar Coordinates Video
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