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?

3

Accepted Answer

Welcome back. I am so glad you're here. We're told the given angle has a radiant measure and it is in standard position identify in which quadrant its terminal side is located. Our given angle is 2.7 and then that's in 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, right? Let's start to draw what we know we can draw a quick sketch of a coordinate plane. 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. We are told that we have an angle in standard position. That means that its initial side begins at the origin and heads toward positive infinity along the X axis. So now what about its terminal side? Well, we recall from previous lessons that when we're in radiance, we know what our 90 degrees is. So that's the positive part of the y axis that is pi divided by two. And we know what our 180 degree angle is in radiance. That's the negative part of the x axis, that's pi and we know what the negative part of the y axis is, that's going to be three pi divided by two. And then if we made it all the way back around to the positive part of the X axis, that would be one full rotation or two pi radiance. And it's helpful to keep in mind what all of these translate to. In terms of real numbers, we know that pi is approximately 3.14 pi divided by two is approximately 1.573. Pi divided by two is approximately 4.71 and two. Pi is approximately 6.28. So we know that our terminal side is at 2.7 radiance, we're going to head counterclockwise from our initial side and then that's going to land us somewhere in the second quadrant because that's between the 1.57 and the 3.142 0.7 is somewhere in between those. So there is our angle of 2.7 radians and we look at our answer choices for quadrant two and that matches with answer choice B 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?

3

Key Concepts

Radian Measure and Angle Conversion

Standard Position of an Angle

Quadrants of the Coordinate Plane

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