00:01
So in this problem, the first we want to do is pick out which of the following graphs would represent the polar coordinate 10 and 5 pi over 6.
00:07
Remember, the 10 refers to the radius or this distance away from the pole.
00:12
And 5 pi over 6 represents our theta value.
00:14
So anytime i would go ahead and graph an angle in polar coordinates, i always start with my angle.
00:20
Well, 5 pi over 6.
00:22
Remember, in terms of radiance, we have 0, pi over 2, pi, 3 pi over 2, and as well as 2 pi.
00:30
Well, 5 pi over 6, that's just a little bit smaller than pi, meaning that it's going to occur in the second quadrant.
00:39
So our angle would be something like this.
00:41
And then we would just go out to this 10 circle, which would be right here.
00:45
Now, if you look at your different answer choices, choice a is in the fourth quadrant, which we know would not be correct.
00:51
B is in the third quadrant, so that would be right.
00:53
C is in the first, and d is the only one in the second quadrant.
00:56
So we know that d is the proper graph.
00:59
Now, for the next couple of questions, for a, we want to rewrite this ordered pair, but where a .r is going to be graded in zero, and our value for theta has to be between 2 pi and 4 pi.
01:12
Well, keep in mind that we have coterminal angles.
01:15
So to get from one coterminal angle to another, we simply need to add 2 pi.
01:18
So one thing i can do to write this coterminal angle is i could take 5 pi over 6 and add 2 pi to it.
01:27
Well, i can put 2 pi over 1 and 2 pi the denominator of 6 would be 12 pi over 6.
01:32
So i would have 5 pi over 6 plus 12 pi over 6, which would equal to 17 pi over 6...