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blagie [28]
1 year ago
15

What is the name of the shape graphed by the function r = 2 cose? O A. Limaçon with inner loop O B. Lemniscate O C. Line O D. Ci

rcle SUBMI
Mathematics
1 answer:
scZoUnD [109]1 year ago
8 0

To understand the function better, let's convert it from polar coordinates to cartesian coordinates. The relation between those coordinates are

\begin{cases}x=r\cos \theta \\ y=r\sin \theta\end{cases}

Our function is

r=2\cos \theta

If we multiply both sides by r, we have

r^2=2r\cos \theta

The square of the radius is equal to the sum of the squares of the cartesian coordinates

x^2+y^2=r^2

Using this identity, we can rewrite our function as

x^2+y^2=2x

Completing the square, we can rewrite our function as

\begin{gathered} x^2+y^2=2x \\ x^2+y^2-2x=0 \\ x^2-2x+y^2=0 \\ x^2-2x+1-1+y^2=0 \\ (x-1)^2-1+y^2=0 \\ (x-1)^2+y^2=1 \end{gathered}

This is a equation of a circle.

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