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A curve in polar coordinates is given by: r=9+3cosθ. Point P is at θ=21π/18 .?
a. Find polar coordinate r for P , with r>0 and π<θ<3π/2 .
b. Find Cartesian coordinates for point P.
c. How may times does the curve pass through the origin when 0<θ<2π?

Respuesta :

Answer:

Step-by-step explanation:

Given that a curve in polar coordinates is given by:

r=9+3cosθ

a) At point P, we have

[tex]θ=\frac{21\pi}{18}[/tex]

Substitute to get

[tex]r=9+cos \frac{21\pi}{18}\\=9.3932[/tex]

b) Cartesian coordinate is

[tex]x= rcos \theta=3.6934\\y =r sin \tjeta =8.6365[/tex]

c) At the origin r =0

when r =0

we have

[tex]9+3cos\theta=0\\cos\theta =-3[/tex]

Since cos cannot take values as -3 it doe snot pass through origin.

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