Plot the point (5, (5x)/(4)) given in polar coordinates, and...

Plot the point \(\left(5, \frac{5x}{4}\right)\) given in polar coordinates, and find other polar coordinates \((r, \theta)\) of the point for which the following are true. \((a) r > 0, -2\pi \le \theta < 0\) \((b) r < 0, 0 \le \theta < 2\pi\) \((c) r > 0, 2\pi \le \theta < 4\pi\) Select the graph that represents the point \(\left(5, \frac{5x}{4}\right)\)

Transcript

00:01 In this question we are given a polar coordinate.

00:03 So polar coordinate are in form r comma theta.

00:07 And the polar coordinate minus r comma theta has same value as r comma theta plus pi.

00:15 So in a part of the question we are given 1 .2 it has same value as minus 1 comma dash.

00:24 So we have to find the value of dash.

00:26 From here we have minus r is equals to 1 and theta.

00:30 Is equal to 2.

00:31 And here we have to find the value of r which is equals to minus 1 and here theta plus pi which is 2 plus pi.

00:40 So from here this is the answer for this dash or we can say the point is minus 1 comma 2 plus pi.

00:49 This is the answer for a part of the question.

00:53 Now moving towards the b part of the question.

00:56 So in b part of this question we are given minus 3 comma square root 2 is equals to 3 comma dash.

01:05 So from here we say that minus r equals to minus 3 and theta is equal to square root 2.

01:12 Minus r changes to r which is equals to 3 and theta changes to theta plus pi which is square root 2 plus pi.

01:20 So this is the value for this fill up and we can say the point is 3 comma root 2 plus pi which is the final answer for b part of the question.

01:32 Moving towards the c part of the question, in c part we are given 3 comma minus pi divided by 4 is equals to dash comma 3 pi divided by 4.

01:46 So from here we have minus r is equals to 3...

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