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# r=sin4theta with rectangular coordinates?

r = 4 sintheta with rectangular coordinates?

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Polar coordinates consists of:

r = radius measure(magnitude)

theta = angle measure(degrees or rad's)

So according to your question, you have stated that r = 4 sintheta :

So the radius(r) = 4*sin(theta)

And Angle measure = theta

To convert the above polar coordinates to Rectangular coordinates:

where Rectangular coordinates = (a, ib)

where a = real number along the x=axis

and ib = imaginary number along the y-axis

i = imaginary number(sqrt(-1)) ( y-axis)

if you remeber your unit circle, and a little bit of trigonometry:

sin(theta) = opp/hyp

cos(theta) = adj/hyp

Hence:

opp = hyp*sin(theta)

adj = hyp*cos(theta)

So since, a = adj

ib = opp

r = hyp

Your Rectangular coordinates ( a , ib)

is now ( r*cos(theta) , r*sin(theta)

Finally: your answer, with r = 4 sintheta

( 4 sintheta*cos(theta) , 4 sintheta*sin(theta)

( 4 sintheta*cos(theta) , 4 sin^2(theta) )

• r = 4 sinθ

multiply both sides by r

Substitute:

r² = 4r sinθ

Substitute:

r² = (x² + y²)

y = rsinθ

(x² + y²) = 4y

x² + y² - 4y = 0

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