- #1
Lebombo
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Homework Statement
r = 3sin[itex]\theta[/itex]
since
x= rcos[itex]\theta[/itex]
x = 3sin[itex]\theta[/itex]cos[itex]\theta[/itex]
and since:
y = rsin[itex]\theta[/itex]
y = 3[itex]sin^2\theta[/itex]
Then I'm sort of stuck..
Lebombo said:Homework Statement
r = 3sin[itex]\theta[/itex]
since
x= rcos[itex]\theta[/itex]
x = 3sin[itex]\theta[/itex]cos[itex]\theta[/itex]
and since:
y = rsin[itex]\theta[/itex]
y = 3[itex]sin^2\theta[/itex]
Then I'm sort of stuck..
Lebombo said:Homework Statement
r = 3sin[itex]\theta[/itex]
since
x= rcos[itex]\theta[/itex]
x = 3sin[itex]\theta[/itex]cos[itex]\theta[/itex]
and since:
y = rsin[itex]\theta[/itex]
y = 3[itex]sin^2\theta[/itex]
Then I'm sort of stuck..
LCKurtz said:You are making it way too difficult. Put ##\sin\theta =\frac y r## in your first equation then see if you can get an xy equation from that.
Lebombo said:Like so:
r = 3sinθ becomes (r=3[itex]\frac{y}{r}[/itex])
= (r =[itex]\sqrt{3y}[/itex]) ?or solving for y, (y = [itex]\frac{r^2}{3}[/itex])
or do you mean something like this:
([itex]\frac{y}{r} = sinθ [/itex]) becomes ([itex]\frac{y}{3sinθ} = sinθ[/itex])= (y = 3sin[itex]^{2}θ[/itex])
A polar equation is a mathematical representation of a curve on a polar coordinate system, where points are defined by a distance from the origin and an angle from the positive x-axis.
Converting a polar equation to rectangular form can make it easier to graph and analyze, especially if the equation involves complex or nested trigonometric functions.
To convert a polar equation to rectangular form, use the following formulas: x = rcosθ and y = rsinθ, where r is the distance from the origin and θ is the angle from the positive x-axis.
Yes, converting a polar equation to rectangular form only works for equations that can be expressed as a function of θ. Equations with multiple values of θ (e.g. spirals or rose curves) cannot be converted using this method.
Yes, you can convert a rectangular equation to polar form using the following formulas: r = √(x^2 + y^2) and θ = tan^-1(y/x). However, some rectangular equations may not have an equivalent polar form.