What is the slope of the tangent line to the polar curve r=2-\cos (\theta) at \theta = \frac...

Question:

What is the slope of the tangent line to the polar curve {eq}r=2-\cos (\theta) {/eq} at {eq}\theta = \frac {\pi}{4} {/eq}?

Tangent Line:

{eq}\\ {/eq}

We can find the slope of a tangent line to the polar curve {eq}r=f(\theta) {/eq} by finding {eq}f'(\theta) {/eq}. In order to find the slope of the tangent line at {eq}\theta=a {/eq}, we can compute {eq}f'(a). {/eq}

Answer and Explanation:

{eq}\\ {/eq}

Given polar curve : {eq}r=2-\cos (\theta) {/eq}

The slope of the polar curve will be:-

{eq}\dfrac{dr}{d\theta}=\sin\theta {/eq}

Now, at {eq}\theta=\dfrac{\pi}{4} {/eq}

{eq}\dfrac{dr}{d\theta}=\sin\dfrac{\pi}{4}=\dfrac{1}{\sqrt 2} {/eq}


Learn more about this topic:

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Tangent Line: Definition & Equation

from NY Regents Exam - Geometry: Tutoring Solution

Chapter 1 / Lesson 11
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