Zenmo
  • Zenmo
Eliminate the parameter to find a Cartesian equation of the curve.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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Zenmo
  • Zenmo
\[x=\sin \frac{ 1 }{ 2 }\theta\] \[y=\cos \frac{ 1 }{ 2 }\theta\] in −π ≤ θ ≤ π
random231
  • random231
square and add.
Zenmo
  • Zenmo
@random231 do u know what −π ≤ θ ≤ π looks like on a graph?

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More answers

Zenmo
  • Zenmo
for (b) Sketch the curve and indicate with an arrow the direction in which the curve is traced as the parameter increases.
random231
  • random231
−π ≤ θ ≤ π is not a curve @Zenmo its a condition
Zenmo
  • Zenmo
what does the condition look like then?
Zenmo
  • Zenmo
actually, what does a negative unit circle look like?
Zenmo
  • Zenmo
|dw:1449481239637:dw|
Zenmo
  • Zenmo
like that unit circle when it is positive, but I don't know what it looks like when the radians are in negative
Zenmo
  • Zenmo
never mind, you answered my first question, I'll open a 2nd question for rephrasing.
random231
  • random231
ill explain
random231
  • random231
so you understood the first part right? that the equation is of a circle?
Zenmo
  • Zenmo
yea
random231
  • random231
fine. now look at the condition −π ≤ θ ≤ π
Zenmo
  • Zenmo
okay
random231
  • random231
it says theta varies from -pi to pi which means it swipes all the way from -pi thru 0 to pi
Zenmo
  • Zenmo
okay
random231
  • random231
so put the value -pi in x=sin1/2θ y=cos1/2θ
Zenmo
  • Zenmo
so i would plot points for x and y from the following: -pi -pi/2 0 pi/2 pi
random231
  • random231
youll get the coordinate from where the circle starts. that is (-1,0)
random231
  • random231
yeah!! :)
Zenmo
  • Zenmo
could you do the first two for me? for -pi and -pi/2
random231
  • random231
so youll actually get a semicirle
random231
  • random231
|dw:1449481881915:dw|
random231
  • random231
x=sin-pi/2=- sin pi/2=-1
Zenmo
  • Zenmo
\[x=\sin \frac{ 1 }{ 2 }(-\pi)\] what value would that be?
random231
  • random231
|dw:1449481997385:dw|
Zenmo
  • Zenmo
\[x=\sin \frac{ 1 }{ 2 }(-\pi)=\sin \frac{ -\pi }{ 2 }=-1\] is that correct?
Zenmo
  • Zenmo
checking to see if i am plugging in the correct values in
random231
  • random231
bullseye!! :)

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