In Exercises 21–26, use a polar coordinate system like the one sh...

Question

In Exercises 21–26, use a polar coordinate system like the one shown for Exercises 1–10 to plot each point with the given polar coordinates. Then find another representation of this point in which a. r>0, 2π < θ < 4π. b. r<0, 0. < θ < 2π. c. r>0, −2π. < θ < 0. (4, π/2)

Accepted Answer

The following point has polar coordinates, plot it in the polar coordinate system, then determine another point that has the same location as the given in which R is less than zero. And theta is between zero and two pi with our point being 93 pi divided by two. Now to solve this, let's first plot our 0.93 pi divided by two, no from zero. We will go counterclockwise until we reach the angle three pi divided by two. So we will go around giving us three pi divided by two. Now our point goes nine in that direction which means we will move down by nine in the direction of three pi divided by two. Now this would be our point in the polar coordinate system. Let's find another point that has the same location. Now to do this, we want a negative R which means we can find the point negative R theta in which theta is increased by a pi. This will give us a point in the same location with a negative radius. So our R is nine, let's change that to negative nine. Now we want three pi divided by two plus pi, this gives us negative nine five pi divided by two. Now we notice our angle data should be between zero and two pi. However, we have five pi divided by two which is larger than two pi to fix that we can just subtract to to get back in her interval. Fact two pi they give us negative nine I divided by two. This should be a point that has a different angle and a negative radius. But at the same place, we can check it by going in the direction of pi divided by two and going negative nine on our radius, which means we go directly downwards by nine, which is where our point is. OK. I hope to help you solve the problem. Thank you watching. Goodbye.

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In Exercises 21–26, use a polar coordinate system like the one shown for Exercises 1–10 to plot each point with the given polar coordinates. Then find another representation of this point in which a. r>0, 2π < θ < 4π. b. r<0, 0. < θ < 2π. c. r>0, −2π. < θ < 0. (4, π/2)