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?

4

Accepted Answer

Welcome back. I am so glad you're here. We are told the given angle has a radiant measure and it's in standard position identify in which quadrant its terminal side is located. And we're given an angle of 3.8 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 and see what we're dealing with. Here, we have a vertical Y axis. 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. We're told that our angle is in standard position, which means its initial side begins at the origin and heads toward positive infinity along the positive part of the X axis. And now it's going to head from that initial side, counter clockwise 3.8 radiance. But how far is that? Well, we recall from previous lessons that we know what each of these quadrant angles are measured. As in radiance, we know that 180 degrees or the negative part of the X axis is pi radiance. And so the positive part of the Y axis heading straight up is half of that. It's pi divided by two radians. And the negative part of the Y axis is going to be three pi divided by two radians if we make it all the way around one full rotation. So back to the positive part of the X axis, that's two pi radians. And you can plug into a calculator to find out what those are equivalent to in numbers. Pi divided by two is approximately 1.57. Pi is approximately 3.14 three. Pi divided by two is approximately 4.71 and two. Pi is approximately 6.28. So if we're talking about 3.8 radians, that's between 3.14 and 4.71. So from the initial side, we'll head counterclockwise until we get to the third quadrant. And it's somewhere in the third quadrant, we draw a terminal side heading toward negative infinity for both the X and Y values. There is our 3.8 radiance. So we are in quadrant three, we look at our answer choices 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?

4

Key Concepts

Standard Position of Angles

Quadrants of the Coordinate Plane

Radian Measure

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