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Identify and sketch the curve r 6 cos @ 8 sin 0 given in polar equation by transforming to rectangular coordinates....

Question

Identify and sketch the curve r 6 cos @ 8 sin 0 given in polar equation by transforming to rectangular coordinates.

Identify and sketch the curve r 6 cos @ 8 sin 0 given in polar equation by transforming to rectangular coordinates.



Answers

Sketch the curve in polar coordinates. $$ r=6 \sin \theta $$

We want to sketch the following curve and polar coordinates. So given our equal six coastline data, So think about this are equal six. How excited they don't but we're not going to drop it yet. So we know this form. We know this is gonna be a circle. The co sign tells us that this is going to be um not centered at the origin. Rather it's going to be along the X. Axis and it's going to be along the positive X. Axis because this is a positive value, not a negative value. We know the diameter is going to be six. And the reason we know that is because coastline is maximized its its biggest value at one and that's when this is equal to 00 radiance. So and this is zero radiance. We get this whole thing is one which means six times 26. So at zero radiance we have a And our value of six. So when we graph this we see that six is the maximum value giving us a diameter of six and a radius of three.

This equation or you call six type school system setup, but let's cover this into the rectangular form. Okay? So the first step that's multiply our to both sides of the equation. So I get R squared equals six times, are times cozy. Um say to okay. According to the conversion formula with the R squared is equipment as I squared plus Y squared and art hubs. Cosell's say that You call six times hacks. Okay, So we know this is uh, equation of a circle. Okay?

This was sure. Um, you really vision in court, card holder for manure going through our vision for the unit. Question is are you also six? Cost a gun less? It's a Well, we have good words. No, Kardashian isn't for everyone to make a on that English. You would say you come on this way. 60. Go on. Must be 80. Do on ST Peter. Okay, So that you are spreading mingling the your like space x respect this rice plate six in Iraq also, you know that next. Plus, I find it amusing. Another this for my little equation, Young like if you simplified the secretion for them in Texas. My anticipation is six. This will, I swear. I just need wait. Now you seem to make it perfect for what you have in the billions. Actually, I no idea. Four years for this president, A 16 year and 16 years ago, Daisy Day. These Tito's way going to think these we come from here, they become explainers tea with strapless. Why minus four months? Whether because for everything you see is a Grecian full circle, I would say them Kiko more four and radius. You just light you okay?

The problem is sketches a curve with the Cuban police question first, sketching the graph of R as a function with theater in Kardashian coordinates. R is equal to two terms. Sign six times data by using some grafting tools, and it's easy to draw a graph of R as a function of the tar in Kardashian. Corniness says this is just a the trig function. Now let's see how two jobs the Graf was a curve. But is that given polar your creation first, the ways I say that Look, when Peter goes from zero to hi or what? Twelve. Our ghost goes from zero to two. Silver can jars a graph Luck. This on the one data goes from hi. Over twelve to Piola six. Our goes from to zero so they can lock this on the one thing that goes from Piola six to Pyla for our goes from zero to negative too. Things I s negative. So which are you and there axe access. We can draw black this now. Now, similarly, we can job, uh, other parts. Finally, we can gut the following rough, so it it looks like thiss. This is a graph of the cure of, but given polar coordinates


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