Hi! Good Afternoon. Can someone help me about the area of polar coordinates?

I saw in a certain example that the interval Of the equation r=2-sinΘ and r=3sinΘ is Π/6≤Ɵ≤Π/2.
Can someone explain how it becomes?

Question

Hi! Good Afternoon. Can someone help me about the area of polar coordinates?

I saw in a certain example that the interval Of the equation r=2-sinΘ and r=3sinΘ is Π/6≤Ɵ≤Π/2.
Can someone explain how it becomes?

aravindg · Answer

hey welcome to openstudy !!

anonymous · Answer

Can you answer my question. Thank you

zepdrix · Answer

The inverval of the equation? Hmm I'm not quite sure what that means. Here is a nice pretty graph of the two functions. https://www.desmos.com/calculator/xlhjges48e It seems they intersect at $\large \theta=\pi/6$ and again at $\large \theta=5\pi/6$.

anonymous · Answer

yes. it intersects at  θ=π/6 and again at θ=5π/6, but the interval that i posted is also right? is it? then i will just multiply it by 1/2? am i right?

zepdrix · Answer

What are you trying to do exactly?
Find the area of the intersecting regions?

If so, then yes you could do that. Setup your interval from $\large \pi/6$ to $\large \pi/2$ and just multiply the by $\large 2$ since the area is symmetric up there.

anonymous · Answer

yes, that was exactly what i mean..
but, is there any formula to find the intersecting regions?

zepdrix · Answer

For finding points of intersection?
$$\large r=2-\sin \theta \qquad \qquad r=3\sin \theta$$

Set your two equations equal to one another,$$\large 2-\sin \theta=3\sin \theta$$
And then solve for $\large \theta$. We will do so by first solving for $\large \sin\theta$ and from there remembering our special angles.


Add sin theta to both sides,$$\large 2=4\sin \theta$$Divide by 4,$$\large \frac{1}{2}=\sin\theta$$
Can you recall what special angle produces 1/2 from the sine function? :D

zepdrix · Answer

Those are special angles on the unit circle c:

$\large \sin \dfrac{\pi}{6}=\dfrac{1}{2}$

$\large \sin \dfrac{5\pi}{6}=\dfrac{1}{2}$


You should definitely have the unit circle memorized if you're doing this for a school class c: Yah you might be able to get the angle by arcsine, if you have a good calculator it might even give it to you as a nice fraction instead of a messy decimal.

anonymous · Answer

okay i think i remember those special angles. but i did not memorize it..

by the way, can you give me an example that  i can practice to solve at home afterwards? if its okay. :D