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anonymous
 5 years ago
1. Algebraically transform r = 8sinθ into a Cartesian equation of a circle (in standard form).
anonymous
 5 years ago
1. Algebraically transform r = 8sinθ into a Cartesian equation of a circle (in standard form).

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amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0algebraically eh.....

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0r = 8sin(t) is a straight line right?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0I see it :)...polars still get me a little lol

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0lets do I table to see where it going ...can we do that? t = 0,45,90,360....

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0when its at 90; or straight up, we get r = 8 so this is a circle about the y axis with a radius of 8 centerd 4 below the origin...

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0but I am prolly messing that up still....

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0well in my textbook theres a question similar to this, but i dont know how to get the last equation. r=6sinθ r²=6rsinθ x²y²=6y x²6y+9+x²=9 (y3)²+x²=3²

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0yeah, I was gettin to that :) just wanted to make sure I had an answer key to go by ;)

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0our equation is going to end up as: x^2 + (y+4)^2 = 16 r = 8sin(t)

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0r = 8sin(t) ; muliply by r r^2 = 8rsin(t) ; convert to cartesians x^2 + y^2 = 8y ; +8y x^2 + y^2 +8 = 0 ; complete square for "y" x^2 + y^2 +8y +16 = 16 ; convert to circle equation x^2 + (y+4)^2 = 16 ; tada!!!

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0you see thats a typo ...8y*

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0At which step? and where did the 16 come from?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0by now you should be familiar with a process called "completing the square". remember it?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0step 4 I put in 8 instead of 8y ;)

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0a complete square can be transformed back and forth between to ...... forms.

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0(x+4)^2 = x^2 +8x +16 right? we can easily move back and forth between these equations since the are equal to each other...

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0but what is usually missing in order to "complete" a sqaure is this: (x+___)^2 = x^2 +8x + ______

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0we need 2 numbers that are exactly the same, that add to get 8. what numbers are they?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0good :) 4+4 = 8, that will satisfy that middle term; now we multiply 4*4 to get the last term. 4^2 = 16 (x+4)^2 = x^2 +8x + 16 you see where we got it now?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0x^2 + 6x + ____ what would we complete the square with here?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0real close....look again. 3+3 = 6 3*3 != 12

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0good :) we need to add 9 to "complete" the square what happens when you add a number to one side of an equation? what do we do to the other side?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Add it on the other side

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0Exactly :) Do you see where I did that in the problem? x^2 + y^2 +8 = 0 ; complete square for "y" x^2 + y^2 +8y +16 = 16

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0i really should fix that typo lol

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Haha no. That's where I'm stuck.

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0x^2 + [ y^2 +8y +____] = 0 ; complete square for "y" what number do we use to "complete" the square for y?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0its always gonna be half the middle term and then square it

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.08/2 = 4 > 4^2 = 16 :) good

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0x^2 + [y^2 +8y +16] = 0 + 16 ^^^ ^^^ we add 16 to both sides righ there right?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0then we just clean it up: x^2 + (y+4)^2 = 16

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0which agrees with what we drew in the first place ;)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Where did the 8y go then?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0remember we can move between the forms of a complete square? (y+4)^2 = y^2 +8y +16 we just use the one for the other.... they are identical in value, they only look different in form.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Ohhh ok. I get it now!!

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0once we got a "complete" square, we use it to clean up the equation ;)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Ok, I finally understand this now! Thanks for helping me out!
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