welcome back mathematicians in this video we are going to do a few more examples where we work with radians before we look at these examples i want to remind everyone that 180 degrees is actually equal to pi radians if we were to divide both sides by 2 we would then get 90 degrees is equal to pi over 2 radians so we are now going to go ahead and put these angles in standard position on the coordinate planes so we start with 7 pi over 8. what i would want to remind everyone is that the positive x-axis is 0 degrees which is 0 radians the positive y-axis is 90 degrees which as we just mentioned is pi over 2 radians the negative x-axis is 180 degrees which is pi radians and finally the negative y-axis is 270 degrees which would be 3 pi over 2 radians now we have to go ahead and plot 7 pi over 8 on the coordinate plane to do this we will start with the vertex on the origin the initial side on the positive x-axis the question is where is the terminal side located probably the easiest way to look at this is to think of 7 pi over 8 as 7 8 times pi and to look at these angles on the each axis as one-half times pi one times pi and three halves times pi and what you're really asking is to compare 7 8 to all these other fractions in the coordinate plane is 7 8 between 0 and 1 half no it's larger than one half is 7 8 between one half and one yes yes it is so therefore we are going to put the terminal side in quadrant number two and so this is our angle seven pi over eight again this is a sketch it's not a hundred percent accurate it's just simply a sketch let's go to the second problem now the second problem we notice is an angle in terms of radians but it's negative which means we are going to have clockwise rotation so i'm going to go ahead and mark my my angles on my axes but i'm going to go in clockwise rotation so the positive x-axis is still zero the negative y-axis is now going to be negative pi over two the negative x-axis is negative pi and then finally the positive y-axis is negative three pi over two from here i'm going to go ahead and plot my vertex and initial side now the question is where is negative three fifths located when you compare it to the angles that i've marked on the coordinate plane well negative three-fifths is going to be between negative one-half and negative one so therefore the terminal side will be in quadrant number three with the rotation being clockwise finally let's go ahead and look at five pi over four so again i'm going to mark my angles but because i'm going in counterclockwise rotation i'm marking them as positive angles so the positive y axis is pi over two negative x-axis is pi radians and the negative y-axis is 3 pi over 2 radians i'm going to start by making my vertex and my initial side now the question is where does my terminal side lie well my terminal side is going to be at five pi over four five fourths is larger than one but less than three halves so therefore five fourths or five pi over four will be in quadrant number three so this is going to be counterclockwise rotation all the way to count to quadrant number three alright guys good luck