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.

(7.4, 2.5)

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 po the polar coordinates given are 13.4 comma 5.3. Now the answer choice is provided all represent different versions of the rectangular coordinates with answer choice A being 8.3 comma negative 9.7. Answer choice B being 12.8 comma 7.9 as jo C being 7.4 comma negative 11. and answer choices D being 8.3 comma negative 6.5. Now for a question like this one where we know we're going to be changing from polar coordinates to rectangular coordinates, we just recall a or, or we have to think about first how exactly each of those versions are written. So we're going polar to rectangular. So polar coordinates are written as open parentheses. R comma theta where R is a radius and the is an angle. And that will be changed to rectangular coordinates which is written as open parentheses X comma Y closed parentheses. Now we have some formulas that are very helpful with this change where we know that the X coordinate is equal to R multiplied by cosine of theta. And the Y coordinate is R multiplied by sign of theta. So therefore, we have that X is equal to our R is 13.4. So we have X equals open parentheses, 13.4 closed parentheses multiplied by cosine of our theta 5.3. And if we plug that into our calculator, this will round up to be around 7.4 and our Y coordinate will be equal to open parentheses, 13.4 closed parentheses multiplied by sine of our theta which is 5.3. And once again, once we plug that into our calculator, we'll have a rounded answer of around negative 11. which means that our porter coordinate or our rectangular coordinate will now be 7.4 comma negative 11.2. And that will be our answer for this question which matches with answer choice C and we can see how easy it could be with just using two simple formulas, how we can change from polar coordinates to rectangular coordinates. 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. (7.4, 2.5)