Video Transcript
What is the reference angle for negative 330 degrees.
We will begin by sketching the unit circle and identifying where the angle negative 330 degrees lies. For any angle in standard position, we measure from the positive 𝑥-axis. And if the angle is positive, we measure in a counterclockwise direction. If the angle is negative as in this question, we measure in a clockwise direction. We can mark on negative 90, negative 180, negative 270, and negative 360 degrees. Negative 330 degrees lies in the first quadrant between negative 270 and negative 360 degrees.
Next, we recall that if 𝜃 is an angle in standard position, then the measure of the acute angle the terminal side makes with the 𝑥-axis is called the reference angle of 𝜃. And it is this angle we’re trying to calculate in this question. We will call this angle 𝛼. The sum of the magnitude of the directed angle 𝜃 together with the reference angle 𝛼 is a full turn or 360 degrees. In this question, the magnitude or absolute value of negative 330 degrees plus 𝛼 equals 360 degrees. Since the absolute value of negative 330 degrees is simply 330 degrees, we have this angle plus 𝛼 equals 360 degrees.
We can then subtract 330 degrees from both sides, giving us 𝛼 is equal to 30 degrees. This is the reference angle for negative 330 degrees.
