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anonymous
 one year ago
Polar coordinates of a point are given. Find the rectangular coordinates of the point. (5, 180°)
a. (5,0)
b. (0,5)
c. (0,5)
d. (5,0)
anonymous
 one year ago
Polar coordinates of a point are given. Find the rectangular coordinates of the point. (5, 180°) a. (5,0) b. (0,5) c. (0,5) d. (5,0)

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SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.0\(y=r\cdot \sin(\theta)\) \(x=r\cdot \cos(\theta)\)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.0You are given that: \(r=5\) \(\theta = 180^\circ\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Sorry, I am teaching myself. I am somewhat confused. I need help.

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.0This is in general: \(y=r\cdot \sin(\theta)\) \(x=r\cdot \cos(\theta)\) (if you want to know why these values are what x and y are equivalent to, then let me know) And in our case, \(y=(5)\cdot \sin(180)=(5)\cdot 0=0\) \(x=(5)\cdot \cos(180)=(5)\cdot(1)=5\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I am writing this down.

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.0dw:1444238217960:dw

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.0The length of the base is x, and the length of the side is y. This is (roughly) how cartesian coordinates are represented (ok?)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I am still here. I am writing this down.

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.0And polar coordinates are represented differently: You face the direction of \(\huge _{^\theta}\) and you walk in this direction \(\huge _{^{_r}}\) units long.

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.0If you have questions about anything that I am posting, please ask....

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.0as it is now I will assume you got no questions.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I am understanding well.

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.0And based on the diagram 9above), you can see that: \(\sin(\theta)={\rm opposite/hypotenuse}=y/r\) \(\cos(\theta)={\rm adjacent/hypotenuse}=x/r\) (this is simple trigonometry) Now, multiply both sides of each equation times r. You will get: \(\displaystyle \color{red}{ r \times}\sin(\theta)=\color{red}{ r \times}\frac{y}{r}\) \(\displaystyle\color{red}{ r \times}\cos(\theta)=\color{red}{ r \times}\frac{x}{r}\) (r cancels on the right side of each of the equations) \(\displaystyle r\sin(\theta)=y\) \(\displaystyle r\cos(\theta)=x\)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.0Thus, knowing the angle, you can convert any polar coordinate to cartesian coordinate (just as we did in the example ` (5, 180°)` )

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.0I mean: knowing the angle and the radius.

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.0Are you doing calculus with polar coordinates, or this is some other course?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.0Oh, cool. You will encounter it more in calculus, but as it is right now, good luck!

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.0And if anything there are many people who are willing to help with stuff.....
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