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.
$$\alpha=610^{\circ}$$

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Key Concepts

Coterminal Angles

Coterminal angles are angles that, despite possibly having different measures, share the same terminal side when drawn in standard position. This property means that adding or subtracting a full 360° rotation (or 2? radians) any number of times will result in an angle that has the same position as the original angle. This concept is useful for reducing an angle with a large measure to an equivalent angle within a standard interval, typically between 0° and 360°.

Quadrant Classification

Quadrant classification involves determining in which of the four regions (quadrants) formed by the x and y axes in a coordinate plane the terminal side of an angle lies. This depends on the angle’s standard measure, where angles between 0° and 90° lie in the first quadrant, 90° to 180° in the second, 180° to 270° in the third, and 270° to 360° in the fourth. Understanding this classification is essential in trigonometry for determining the sign and value of trigonometric functions.

Transcript

00:02 All right, in number 13, we're told that alpha is 610 degrees.

00:08 And what we're being asked to do is basically classify the angle by quadrant, as they put it.

00:15 So all that means is in which quadrant does the terminal side lie.

00:21 And then we also want to find the equivalent co -terminal angle that's within one revolution of the circle or within the unit circle.

00:31 Close from all we get it that way.

00:32 So basically the coterminal angle that's between zero and 360 degrees.

00:38 So first things first, you got to know that each axis, obviously on the unit circle or even just the x, y grid, is 90 degrees, right? so we're just going to count by multiples of 90 until we can figure out where 610 degrees is.

01:01 Okay.

01:02 So all angles.

01:02 Start with a initial side of the positive x -axis.

01:09 And so here we go.

01:09 Let's see if we can figure it out.

01:10 So there's all the way around that's 360.

01:15 No, didn't want to hold it there.

01:16 Sorry.

01:18 All the way around is 360.

01:20 And now let's count by 90s until we can narrow down where 610 is, right? so 360 plus 90.

01:30 That's 450...