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?

7

Accepted Answer

Welcome back. I am so glad you're here. We're told 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 nine radiant. 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. I'm going to start by drawing a rough sketch of a coordinate plane so we can visualize what's going on here. We've got 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're told our angle is in standard position, which means that its initial side begins at the origin and heads out toward positive infinity along the positive part of the X axis. And so our nine radiance angle is going to head counterclockwise from that initial side. But how far is it going to go? Well, we recall from previous lessons that we know the quadrant measures of our angles. And so we can label this one full rotation all the way around would be two pi radiance. So that's back on the positive part of the X axis half of that half of two pi. So the negative part of the X axis is just pi half of that. So that's the positive part of the Y axis is pi divided by two and three quarters of a rotation around three quarters of two pi. So this is the negative part of the Y axis is three pi divided by two. And you can plug any of those into a calculator to see what those are approximately in numbers. So two pi is approximately 6.28 pi divided by two is approximately 1.57. Pi is approximately 3.14 N three. Pi divided by two is approximately 4.71. So where is nine radiance? Well, going all the way around is 6.28 radiance nine is even bigger than that. So nine radiance is more than one rotation. So we can find a co terminal angle by subtracting one full rotation. So we're going to take nine radiance minus one full rotation, which is two pi radiant and nine minus two pi is approximately 2.72. So 2.72 radiance is co terminal with nine radiance and that does fall within the numbers that we have here 2.72 is in between 1.57 and 3.14. So we can draw our terminal side. We had counter clockwise from our initial side heading somewhere into quadrant two, heading out toward negative infinity for our X values and positive infinity for our Y values. That's our nine radiance. 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?

7

Key Concepts

Standard Position of an Angle

Radian Measure and Its Relation to Quadrants

Quadrants of the Coordinate Plane

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