Question

Write the following polar equation in Cartesian coordinates:

2r(sin θ + cos θ) = 5.

b) find the y-intercept and slope

Answer 1

What have you tried? Do you know the conversions? This one jumps right out at you if you do.

Answer 2

I divided both sides by 2, and got the y-intercept to be 5/2. I'm not sure of the conversion so I'm a bit confused..

Answer 3

WAY too hard.

\(x = r\cos(\theta)\), right?

Answer 4

I also have another with Write the following polar equation in Cartesian coordinates:

r = sin (2θ) but i'm stuck

Answer 5

Yes x= r cos theta and y = r sin theta

Answer 6

One at a time, please.

Okay, now use your Distributive Property to get rid of the parentheses.

Answer 7

r sin (θ) + r cos (θ) = 5/2

Answer 8

so that should be equivalent to x + y = 5/2?

Answer 9

This was just waiting for you not to see it. Now, answer the question about as fast as youcan write it, right?

Slope =
y-Intercept =

Answer 10

slope = -1 and y-intercept = 5/2

Answer 11

how will I write the cartesian coordinate?

Answer 12

Good work.

Repost the other one and tag me. We can talk there.

Answer 13

ok thank you

Answer 14

Write the following polar equation in Cartesian coordinates:

r = sin (2θ) becomes

Answer 15

I do not see exactly how to proceed. My recommendation under that circumstance is to give something a shot and see where it goes.

We have some fundamental clues.

\(x = r\cos(\theta)\)

\(y = r\sin(\theta)\)

One more thing comes to mind that might be helpful.

\(\sin(2\theta) = 2\sin(\theta)\cos(\theta)\)

How can we get all that together?

Answer 16

x= sin 2θ (cos θ)
y=sin 2θ (sin θ)

Answer 17

?? I don't see that.

Answer 18

\(r = 2\sin(2\theta)\)

\(r = 2(2\sin(\theta)\cos(\theta))\)

\(r = 4\sin(\theta)\cos(\theta)\)

Answer 19

As in, I don't see that getting us anywhere. What can we do with mine?

Answer 20

\[x^2 ++ y^2 = (\sin 2θ)^2 * (\cos θ)^2 + (\sin 2θ)^2 * (\sin θ_^2\]
\[= (\sin 2θ)^2 = \sin 2θ * \sin 2θ = \sin 2θ (2 \sin θ \cos θ)\]

Answer 21

You're making a mess. Is that getting anywehre?

\(r = 4\sin(\theta)\cos(\theta)\)

If \(r \ne 0\)

\(r\cdot r^{2} = 4r\sin(\theta)r\cos(\theta)\)

\(r\cdot (x^{2}+y^{2}) = 4yx\)

Are we closer or still just wandering around?

Answer 22

Still a bit confused

Answer 23

Remember the "Fundamental Clues". I didn't mention \(r^{2} = x^{2} + y^{2}\).

These are our ONLY conversion tools. We have to manipulate things to get those structures. That's all I did. After the double angle formula, I just used the three Fundamental Clues.

Answer 24

ahhh I seee it

Answer 25

Thank you @tkhunny

Answer 26

You still have to get rid of the last 'r'. \(r = \sqrt{x^{2} + y^{2}}\). You may wish to square some things and make it look prettier.