# Math Help - Finals. Quick polar questions

1. ## Finals. Quick polar questions

Alright. Thank you very much for your help in advance. I went thru all these problems myself and had questions on these particular ones. They shouldn't be too bad.

1) Convert X^2-y^2=1 to Polar...
.... so it will = (r^2)(cos^2theta) - (r^2)(sin^2theta) =1
r= sqrt(1/(cos^2theta-sin^2theta))
where from here?

2) Convert r=3sintheta to cartesian.
would x^2 + y^2 = 3y be correct?

3) What is the area of r^2=4cos2theta ??

4) What is the area of the region that lies inside the first curve and outside the second curve
curve one = r=3costheta. curve 2 = r= 1+costheta

5) What is the area of the region that lies inside both curves
1.st = r=sin2theta second = r=sintheta.

6) Find the solutions of the equations (now into complex number stuff) ..
2x^2 -2x +1 =0

7) Converting from complex numbers to polar form...
does -3+3i = (Sqrt(18))cis(tan(-1))

8) lastly, can someone provide a problem which wants me to convert from polar to complex? like... how rcostheta = a and risintheta = b

THANK YOU! If you answer these questions it will help my studying a LOT!
I just went 4 hrs studying other math stuff.
THANK YOU again!

2. 4) What is the area of the region that lies inside the first curve and outside the second curve
curve one = r=3costheta. curve 2 = r= 1+costheta
You can find the region in the first quadrant and multiply by 2 because of symmetry.

$3cos(t)=1+cos(t)$

Solving this tells us that they intersect at Pi/3.

$\int_{0}^{\frac{\pi}{3}}\left[(3cos(t))^{2}-(1+cos(t))^{2}\right]dt$

3. Galactus, you sure about the starting and the ending? If i remember correctly one of those lines takes 2pi to make a full cycle and the other one 1pi ?

4. Originally Posted by 3deltat
Galactus, you sure about the starting and the ending? If i remember correctly one of those lines takes 2pi to make a full cycle and the other one 1pi ?
Galactus is correct. Draw the two curves (circle and cardioid) and see it for yourself.

5. Originally Posted by 3deltat
Alright. Thank you very much for your help in advance. I went thru all these problems myself and had questions on these particular ones. They shouldn't be too bad.

1) Convert X^2-y^2=1 to Polar...
.... so it will = (r^2)(cos^2theta) - (r^2)(sin^2theta) =1
r= sqrt(1/(cos^2theta-sin^2theta))
where from here?

Mr F says: Use a double angle formula ....

2) Convert r=3sintheta to cartesian.
would x^2 + y^2 = 3y be correct?

Mr F says: Yes. Myself, I'd then write it in the form x^2 + (y - k)^2 = r^2 ....

3) What is the area of r^2=4cos2theta ??

Mr F says: See equations (13) - (15) of Lemniscate -- from Wolfram MathWorld (you should think about why integrate from -pi/4 to pi/4).

4) What is the area of the region that lies inside the first curve and outside the second curve
curve one = r=3costheta. curve 2 = r= 1+costheta

Mr F says: Done by Galactus.

5) What is the area of the region that lies inside both curves
1.st = r=sin2theta second = r=sintheta.

Mr F says: Draw a diagram. Think about how Galactus did the previous one.

6) Find the solutions of the equations (now into complex number stuff) ..
2x^2 -2x +1 =0

Mr F says: Use the quadratic formula.

7) Converting from complex numbers to polar form...
does -3+3i = (Sqrt(18))cis(tan(-1))

Mr F says: Draw an Argand diagram. The argument is clearly 3pi/4.

8) lastly, can someone provide a problem which wants me to convert from polar to complex? like... how rcostheta = a and risintheta = b

Mr F says: You mean convert from polar form to Cartesian form. Go to any textbook that covers this material. Or use google.

[snip]
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