Write the polar equation in rectangular form.

Question

Write the polar equation r = 5 sin 0 in rectangular form.

Answer 1

If this angel is theta

the answer is 

First of all you need to know the three equation and put it in you mind which are

x²+y²=r²   ,     x=r * cos(Θ)   ,   y=r * sin(Θ)  so, 

Make sure that in every math question no matter what you will start from what data you have, 

 

so you have r=5 sin(Θ)  multiply the both sides with r

you will have :   r²=5*r*sin(Θ)  ,  But we know that  y=r * sin(Θ)  and x2+y2=r2 So,

x²+y²=5y  ⇒ x²+y²-5y=0    ⇒    x²+(y-5/2)²-25/4=0   ⇒   x²+(y-5/2)²=(5/2)²    
this is the rectangular form 

Answer 2

To convert to rectangular form, we can use the formulas r² = x²+y²,

x = rcosθ, y = rsinθ.

 

r = 5sinθ

 

Multiply both sides by r to get r² = 5rsinθ

 

So, x²+y² = 5y

 

     x² + y²-5y = 0

 

     x² + y²-5y+25/4 = 25/4

 

    (x-0)²+(y-5/2)² = 25/4

 

This is a circle with center (0,5/2) and radius 5/2