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2. Find Carlesian equation for the curve described by the polar equation it to sketch the graph.and use 3 sin 0+4cos...

Question

2. Find Carlesian equation for the curve described by the polar equation it to sketch the graph.and use 3 sin 0+4cos

2. Find Carlesian equation for the curve described by the polar equation it to sketch the graph. and use 3 sin 0+4cos



Answers

Sketch the curve with the given polar equation by first sketching the graph of $ r $ as a function of $ \theta $ in Cartesian coordinates.

$ r = 2 + \sin 3\theta $

So one reason why we really want to use polar coordinates as opposed directing our coordinates is when we're dealing with circular graphs, graphs with some kind of radius or graphs with some kind of angle measure that we're focusing on. And this is going to be the case. Um, with this problem in particular, these types of polar equations, polar graphs are really helpful and useful in applications with a lot of areas of science and engineering. So it's important that we look in those things because they really do have a lot of really world applications. So the graph is three co signed to theta. So if you look at this craft, we know that since the coastline graph is going to be dealing with the X coordinates, um, it'll lie on the X axis, and we see that this graph in particular is going to be a four pedal um graph. So the three value indicates that there will be three as the constant maximum value of the radius. And then we see that because we have this tooth data, we're gonna have all these different pedals in our graph. Eso We see that just by moving around some angles and some coefficients, we can make a lot of different, different, uniquely shaped graphs

Mhm. In this problem we need to find the polar equation for the curve represented by the Cartesian equation. X equals three. Now we know that X is simply equal to our times the co sign of data in polar coordinates, so we'll make the substitution and we can do some cross multiplication. So we get our equals three times one over go sign of data, and we know that one over cosine of theta is just the second of data. So I required equation in polar form is R equals three times the cost of the second of data.

Broken 13 are is a per toe to co sign three theater. They are over the fatal the opportunity of six Science three fade out or is equal to zero. Toko sign three. Feta is equal to zero for faith is ableto boy over six boy over to five boy over overseas they are Overbey. Fator is not people to zero at boy over six for over two by by over six. And there are equations, octane Geant and think there's equal toe over things. However two and my over. If I put old receipts. If we're trying to get this the graph, it will be like a flower with three bidders. Where is very is is to

I was given a question like unheard business. White hands Hot sign. Victor, Is it going toe? One last three hard cost data not taking our common. We can write this. Assigned theta minus three cost data. It's 4 to 1. So how did you goto one by scientists minus three. Boston. So now this It doesn't require the question in Wana foreigners.


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