How do you convert $r = 4 csc (θ) cot (θ)$ $r = 4 csc (theta) cot (theta)$ to rectangular form?

Question

How do you convert $r = 4 csc (θ) cot (θ)$ $r = 4 csc (theta) cot (theta)$ to rectangular form?

1 Answer

Impact of this question

13237 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-05-07T08:58:47

$y^{2} = 4 x$ $y^2 =4x$

Explanation:

If the rectangular coordinate of a point be $(x, y)$ $(x,y)$ and its corresponding polar coordinate be $(r, θ)$ $(r,theta)$ then we know that $x = r cos θ and y = r sin θ$ $x = rcostheta and y = rsintheta$

Our given equation in polar form is
$r = 4 csc (θ) cot (θ) = \frac{4}{sin θ} \cdot \frac{cos θ}{sin θ}$ $r = 4 csc (theta) cot (theta)=4/sintheta*costheta/sintheta$
$\Rightarrow r {sin}^{2} θ = cos θ$ $=>rsin^2theta =costheta$

Multiplying both sides by r
$\Rightarrow r^{2} {sin}^{2} θ = 4 r cos θ$ $=>r^2sin^2theta =4rcostheta$
$\Rightarrow {(r sin θ)}^{2} = 4 r cos θ$ $=>(rsintheta)^2 =4rcostheta$

Putting $r cos θ = x and r sin θ = y$ $rcostheta=x and rsintheta=y$ we have the equation in rectangular form

$\Rightarrow y^{2} = 4 x$ $=>y^2 =4x$

Science

Math

Humanities

... and beyond

How do you convert $r = 4 csc (θ) cot (θ)$ $r = 4 csc (theta) cot (theta)$ to rectangular form?

1 Answer

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

How do you convert r = 4 csc (theta) cot (theta)r=4csc(θ)cot(θ) r = 4 csc (theta) cot (theta) to rectangular form?

1 Answer

Explanation:

Related questions

Impact of this question

How do you convert $r = 4 csc (θ) cot (θ)$ $r = 4 csc (theta) cot (theta)$ to rectangular form?