![]() Now, according to the definition of reference angle, we can determine that the reference angle of -23 degree is 23 degree. At the end, we know that the standard angle = -23 degree. Also, starting from the x axis (zero), however, this time we turn the terminal arm to the negative direction. Same as the last example, we draw the standard angle of -23 degree on a xy plane. ![]() This time, we are going to find the reference angle of a negative angle: -23 degree. And we know that the standard and reference angle land on the third quadrant ( or quadrant 3 ) Now, according to the definition of a reference angle, we can determine that the reference angle of 200 degree is 20 degree. We stop turning the terminal arm when it reaches 200 degree, and we get the standard angle. Starting from the x axis (zero), we turn the terminal arm to the positive direction. Same as the last example, we draw the standard angle of 200 degrees on a xy plane. In this question, we are looking for the reference angle of 200 degree. ![]() Now, we can determine the reference angle.īased on the definition of a reference angle, we can determine that the reference angle is 50 degree We stop at 130 degree and get the standard angleįrom the graph, we know that the angle lands on the second quadrant ( or quadrant 2 ). Starting from the x axis (zero), we turn the terminal arm to the positive direction since we are dealing with a positive angle. First we draw the standard angle of 130 degrees on a xy plane. We want to determine the reference angle of a 130 degree angle. Reference Angle: the acute angle between the terminal arm and the x-axis reference angle is always positive. Let's try out a few example questions on how to find reference angles. ![]() Knowing these, you can use them as shortcuts to help you determine around where a reference angle should be and if you're in the right range. When you get to the positive y-axis, you'll get 90° or π 2 \frac 2 3 π radians. It must be less than 90 degree, and always positive.Ī good thing to note before we move on is that when you're on the positive x-axis, the angle is 0° or 360°, which is also known as 2 π 2 \pi 2 π radians. In other words, the reference angle is an angle being sandwiched by the terminal side and the x-axis. Reference Angle: the acute angle between the terminal arm/terminal side and the x-axis. ![]()
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