In Exercises 13 to 18, classify each angle by quadrant, and...

In Exercises 13 to $18,$ classify each angle by quadrant, and state the measure of the positive angle with measure less than $360^{\circ}$ that is coterminal with the given angle.
$$\alpha=-3789^{\circ}$$

Key Concepts

Coterminal Angles

Coterminal angles are angles that share the same initial and terminal sides when drawn in standard position. This means that one angle can be converted into another by adding or subtracting full rotations (multiples of 360°), thereby landing in the same position in the plane.

Angle Reduction (Modulo 360°)

Angle reduction involves finding an equivalent angle between 0° and 360° by applying the modulo operation with 360°. By adding or subtracting full rotations, any given angle, regardless of how large or negative it is, can be simplified to an angle within one complete rotation.

Quadrant Classification

Quadrant classification assigns angles to one of the four regions of the coordinate plane based on the terminal side of the angle in standard position. Each quadrant corresponds to a specific range of angle measures, and identifying the quadrant helps in understanding the angle's geometric and trigonometric properties.

Rotation Direction

The direction of rotation in angle measurement is significant: positive angles indicate a counterclockwise rotation from the initial side, while negative angles indicate a clockwise rotation. Recognizing the rotation direction is essential when working with negative angles and finding their positive coterminal equivalents.

Transcript

00:04 Okay, in number 18 here, we want to do two things.

00:11 We're given that alpha is this really, really small angle, or if you want to look at it, it's a big negative angle, right? negative 3 ,789 degrees.

00:24 And what we want to figure out is in which quadrant does the terminal side of that angle end up? so here's your quadrant numbers again.

00:34 If you need a little fresher, there you go.

00:39 Okay.

00:40 So that's the first part.

00:41 And then once we determine that, we want to know that we want to know the equivalent or the co -terminal angle to negative 3789 that's within the first revolution of the circle or between zero and 360.

01:00 Okay.

01:01 So we can save a little bit of time here because multiples of the, of 360 that size, you don't want to go one at a time.

01:12 Like if you watch some of the other videos in this section, you know what i'm talking about.

01:16 Okay, so there's the initial side of the angle.

01:21 It's always the positive x axis.

01:23 Now, we're measuring negatively this way.

01:28 And when you measure an angle negatively, it goes clockwise from the positive x axis.

01:34 Okay.

01:35 And that's only negative 360 degrees, right? but think about this for a second.

01:42 What happens if we go around that circle, the unit circle, or that circle there, nine more times, right? that would be a total of 10 times around the circle...

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