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, π/2)

Accepted Answer

Hello everybody. I hope you're 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 negative comma three pi divided by two. Now the answer choices all represent different versions of the rectangular coordinates with answer choice A being zero, comma 12 answer choice B being 12 comma zero answer choice C being zero, comma negative 12 and answer choice D being negative 12 comma zero. Now for a question like this, we should focus on how exactly polar coordinates are written versus rectangular coins. So we are going from porter to rectangular and we should see how each of those are written. So porter coordinates are depicted by writing open parentheses are comma the closed parentheses. And that changes to a rectangular coordinate being open parentheses X comma Y. Now in a poor in it, the R represents a radius and the theta represents an angle. Now we also have two very easy formulas that are very helpful when it comes to making this change. So the X coordinate in a rectangular coordinate system is equal to R cosine of data from the polar version. And the Y coordinate in a rectangular coordinate system is equal to R sign of theta. So R multiplied by the sign of the, of the polar coordinate version. Now using this information, we can rewrite and have that Rx component will be equal to open parentheses is negative 12 multiplied by cosine of a three pi divided by two. And this will be equal to zero once we plug into our calculator. But because we also know that cosine of three pi divided by two is zero and anything multiplied by zero is zero. Now, we can move on to the Y coordinate and we'll have that Y is equal to open parentheses, negative 12 closed parentheses multiplied by sine of three pi divided by two. And now we can either use the calculator or recall from our unit circle. That sign of three pi divided by two is negative one and negative one multiplied by negative 12 is positive 12. So this means that our rectangular coins will be zero, comma 12 and that will be your answer or answer choice. A. So we can see how, just knowing how each version of the coordinates are written as well as using two very simple formulas, we can go ahead and switch between polar and rectangular coordinates. So I hope that was helpful. And until next time

In Exercises 33–40, polar coordinates of a point are given. Find the rectangular coordinates of each point. (−4, π/2)

Key Concepts

Polar Coordinates

Rectangular Coordinates

Conversion Formulas

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