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How to find reference angles

What are reference angles? 1. Reference angles defined. 2. How to find reference angles in degree and radian form. This is the fifth video in a series made for high school and college math students. This series focuses on basic trigonometry skills necessary for math success. Timecodes: 0:00 - Opening 0:23 - Introduction 0:39 - 4 Quadrants defined 1:04 - Quadrental angles 2:12 - What is a reference angle? 2:52 - Technique for calculating reference angles 4:30 - Summary of the formulas 5:15 - Example 1: Find the reference angle for 160 degrees 5:50 - Example 2: Find the reference angle for 5PI/3 6:21 - Example 3: Find the reference angle for 930 degrees Partial transcript: We'll begin with some background information. A zero degree angle points straight to the right. A 90 degree angle points straight up. A 180 degree angle points straight to the left. And, a 270 degree angle points straight down. Once you've made a full rotation of the circle you're at 360 degrees, which is coterminal with zero degrees. The angles we just discussed are known as the quadrantal angles. They break up the coordinate plane into four quadrants. Between 0 and 90 degrees is quadrant 1, that's the upper right side. Between 90 degrees and 180 degrees is quadrant 2, that's the upper left side. Between 180 degrees and 270 degrees is quadrant 3, that's the lower left side. And, between 270 degrees and 360 degrees is quadrant 4, and that's the lower right side. Remember, when you're identifying the four quadrants you start in the upper right side and move counterclockwise. 1 - 2 -3 - 4. Similarly, in radians, between 0 and PI/2 is quadrant 1. Between PI/2 and PI is quadrant 2. Between PI 3PI/2 is quadrant 3. And, between 3PI/2 and 2 pi is quadrant 4. So what is a reference angle? A reference angle is an angle made between the terminal side of our original angle and the x-axis. So, we're looking for the acute angle made between our original angle and a horizontal line. Sometimes we denote our reference angles with a special accent mark called prime. So, if our original angle was angle A our reference angle will be called A-prime. And, if our original angle was called angle theta then our reference angle would be called theta prime. ... [Reference information is available to download at] mathquarium.org. Now let's do some examples. For our first example we'll find the reference angle for 160 degrees. 160 degrees is in the second quadrant, meaning that to find the reference angle I need to take 180 degrees and subtract my original angle. That's 180 degrees minus 160 degrees. 180 degrees minus 160 degrees is 20 degrees. That means that theta prime is equal to 20 degrees. Now, let's find the reference angle for 5 PI/3. 5 PI/3 is in the 4th quadrant so to find my reference angle I need to take 2 pi and subtract away my original angle. That's 2 pi minus 5 PI/3 which is the same thing as 6 PI/3 minus 5 PI/3. 6 PI/3 minus 5 PI/3 is PI/3, that means my reference angle is PI/3. Now let's do an example that shows what to do when our angle goes around the circle more than once. Let's find the reference angle for 930 degrees. 930 degrees lands in the third quadrant. This is difficult to tell just from looking at the angle number itself, so the strategy is to find a coterminal angle that lands in the same place. We'd like to find an angle between 0 and 360 degrees that is coterminal to 930. To do that we're going to subtract away 360 degrees until we get an angle that's between 0 and 360 degrees. Starting with 930 degrees we subtract 360 degrees and get 570 degrees. But 570 degrees is still too big so we have to do it again. 570 degrees minus 360 degrees is 210 degrees. That means 210 degrees is coterminal with 930 degrees. Therefore finding the reference angle for 930 degrees is the same problem as finding the reference angle for 210 degrees. So we'll change our problem to find the reference angle for 210 degrees. 210 degrees is in the third quadrant. That means to find the reference angle for 210 degrees I need to subtract my original angle minus 180 degrees. 210 degrees minus 180 degrees is 30 degrees. That means that the reference angle is 30 degrees. Since the reference angle for 210 degrees is 30 degrees, that means that the reference angle for 930 degrees is also 30 degrees. Music in title bumper: Light Stingby Kevin MacLeod is licensed under a Creative Commons Attribution license (https://creativecommons.org/licenses/...) Source: http://incompetech.com/music/royalty-... Artist: http://incompetech.com/ All other music and graphics licensed via Envato Elements: https://elements.envato.com.