Hey, everyone. In this problem, we're asked to use reference angles to complete the missing trig values in quadrants 2, 3, and 4. Now that we know that all these trig values are going to be the same as those in quadrant 1, with just varying signs based on the quadrant, we can do this really quickly. So remember our mnemonic device here of how we remember which function is positive in each quadrant. All students take calculus, telling us the first letter of each function that's positive within each quadrant. Now let's first take a look at quadrant 2, looking at 135 degrees and 120 degrees. These have reference angles of 45 degrees and 60 degrees, respectively, so we could just go ahead and copy those trig values over to this quadrant. So for 135 degrees, I have 2/2, 2/2, and 1. Then for 120 degrees, I have 1/2, 3/2, and the square root of 3 for that tangent. In this quadrant, only the sine is positive based on that mnemonic device, so that means both my cosine and tangent need to be negative here. So my x values of both of these should be negative, as well as the tangent value here on the end. Now, we're done with quadrant 2. Let's move on to quadrant 3 down here.

Now looking at quadrant 3, I have 210 degrees and 240 degrees as those missing trig values. Looking back up to quadrant 1, I know that 210 degrees has a reference angle of 30 degrees, and 240 degrees has a reference angle of 60 degrees, so I can copy those trig values over. So for 210 degrees, I have 3/2 for my cosine, 1/2 for my sine, and 3/3 for that tangent. Then for 240 degrees or 4π/3 radians, I have one-third for the cosine, 3/2 for the sine, and a square root of 3 for that tangent. In this quadrant, only the tangent is positive, so that means both my sine and cosine need to be negative. So x and y here are both negative when looking at these coordinates. Now, finally, let's take a look at quadrant 4 over here.

Now, looking in this quadrant, my missing information is for 330 and 315 degrees, which have reference angles of 30 degrees and 45 degrees, respectively. So, let's go ahead and copy those trig values over here in this quadrant. So for 330 degrees, I have 3/2, 1/2, and 3/3. Then for 315 degrees, I have 2/2, 2/2, and finally, one for that last tangent value. In quadrant 4, only the cosine is positive here, so that tells me that I need to go ahead and make both my sine and tangent negative. So my sine value and my tangent need to be negative for both of these angles. Now we have completely filled in all of our information for the unit circle. Continue to practice this on your own and check in with me as needed. Thanks for watching, and I'll see you in the next one.