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Convert the cartesian equation to a polar equation that expresses r in terms of ? . ( x + 9...

Question:

Convert the cartesian equation to a polar equation that expresses r in terms of {eq}\theta. {/eq} {eq}(x+9)^{2}+y^{2}=81 {/eq}

Eqaution in Polar Form:

To get the equation in polar form from the cartesian form, always use the general relation between the cartesian coordinates and polar coordinates such as:

  • {eq}x=r\cos \theta\\ y=r\sin\theta {/eq}

Simplify the obtained equation using the basic trigonometric property of sine and cosine function.

  • {eq}\sin^{2} \theta+\cos^{2}\theta=1 {/eq}

Answer and Explanation: 1

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Given data:

{eq}\displaystyle (x+9)^{2}+y^{2}=81 {/eq}

Plug {eq}x=r\cos\theta {/eq} and {eq}y=r\sin\theta {/eq} in the above equation.

{eq}\begi...

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Complex Numbers in Polar Form: Process & Examples

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Chapter 24 / Lesson 2
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The polar form of a complex number is an alternative way to write a complex number. The polar form is easy to compute. Examples are provided.


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