Work each problem.

Consider each angle in sta...

Question

Work each problem.

Consider each angle in standard position having the given radian measure. In what quadrant does the terminal side lie?

-2

Accepted Answer

Welcome back. I am so glad you're here. We're told that the given angle has a radiant measure and it's in standard position, identify in which quadrant its terminal side is located. Our given angle is negative 2.5 radiance. Our answer choices are answer choice, a quadrant one answer, choice B quadrant two, answer choice C quadrant three and answer choice D quadrant four. Let's draw a quick sketch of a coordinate plane. So we can see we can visualize what we're dealing with. We have a vertical Y axis and a horizontal X axis. They come together at the origin in the middle, up into the right of the origin is quadrant one up into the left of the origin is quadrant two, down into the left of the origin is quadrant three and down into the right of the origin is quadrant four. Our angle is in standard position which means that its initial side begins at the origin and heads out toward positive infinity along the X axis. And because this angle is negative, it's going to head clockwise from there. But how far is it going to go? Well, we recall from previous lessons that we know the radiant measures of our quadrant angles one full rotation around. And because we're talking negative here, one full rotation around. So back all the way to the positive part of the X axis would be a negative two pie. And then if we were only going halfway, we were heading toward the negative part of the X axis. That would be a negative P. So half of that distance that would be the negative part of the Y axis would be a negative pi divided by two and then the positive part of the Y axis. So three quarters of the way around would be a negative three pi divided by two. And you can plug those into a calculator and see what they are approximately in numbers. Negative pi divided by two is approximately negative 1.57. Negative pi is approximately negative 3.14 negative three. Pi divided by two is approximately negative 4.71 and negative two. Pi is approximately negative 6.28. So where is negative 2.5 in there? Well, that's between negative 1.57 and negative 3.14. So from our initial side, we had clockwise and then we are somewhere in the third quadrant, that's our negative 2.5 radians. So we look at our answer choices for quadrant three and that matches with answer choice C well done. We'll catch you on the next one.

Work each problem.

Consider each angle in standard position having the given radian measure. In what quadrant does the terminal side lie?

-2

Key Concepts

Standard Position of Angles

Quadrants of the Coordinate Plane

Radian Measure of Angles

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