In Exercises 33–40, polar coordinates of a point are given. Find ...

Question

In Exercises 33–40, polar coordinates of a point are given. Find the rectangular coordinates of each point.(4, 90°)

Accepted Answer

Hello everybody. I hope you are doing. All right. Today, today we're going to be looking at this question that states convert the following polar coordinates to rectangular coordinates where the polar coordinates given are 15 comma 270 degrees. Now the choices provided all represent different versions of the rectangular coordinates with a choice or choice A being 15 comma zero. S choice CB is zero, comma 15 at choice C is zero, comma negative 15 and as choice D is negative comma zero. Now, the first thing we'll do is not that we are going from polar coordinates, two rectangular coordinates. So we should know how exactly polar coordinates are written and how rectangular coordinates are written. So when it comes to poder, we have open parentheses. R comma the close parentheses where R is a radius and data is an angle. Now this will can be rewritten in rectangular coordinates, which is the more basic version of coordinates that we should know which is open parentheses, X comma Y closed parentheses. Now, there are two very simple formulas that can help us change between polar and rectangular coordinates where we have that the X component of the rectangular coordinates is equal to R of the polar coordinate multiplied by cosine of theta from the polar coordinate. And we also know that the Y component of the rectangular coordinates is equal to R from the polar coordinates multiplied by sign of data from the polar coordinate. Now, we can use those formulas to plug in the values that we know. So we have that X is equal to open parentheses, 15 closed parentheses multiplied by cosine of 270 degrees. And then we plug this into our calculator. Oh, we simply know that cosine of 270 degrees is equal to zero. We know that the final answer here will be zero because anything multiplied by zero is zero. So we have that our X component will be zero. If we move on to our Y component, we'll have that Y is equal to open parentheses. 15, closed parentheses multiplied by sine of degrees. And once again, we can either use our recall or the calculator to know that sign of degrees is equal to negative one, which means that we'll have 15, multiplied by negative one, which means we have a final answer of negative 15. And once we combine those two answers, we'll have a rectangular cordate of open parentheses. Zero comma negative 15, which will be our answer for this question or answer choice. C so we can see that just simply knowing how to write the different types of coordinates. So polar and rectangular, as well as knowing these two simple formulas, we can switch from polar coordinates to rectangular coordinates in a very quick manner. So I hope that was helpful. And until next time.

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In Exercises 33–40, polar coordinates of a point are given. Find the rectangular coordinates of each point.(4, 90°)

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