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Chapter 5: Problem 22

Sketch each angle in standard position. (a) \(270^{\circ}\) (b) \(-120^{\circ}\)

Short Answer

Expert verified
The angle \(270^{\circ}\) in standard position is along the negative y-axis and the angle \(-120^{\circ}\) in standard position lies in the second quadrant of the coordinate system.

Step by step solution

01

Sketch Helper Lines

First, draw a coordinate system with x and y axes. Remember that the initial axis for standard position is always the positive x-axis.
02

Sketch the Angle \(270^{\circ}\)

Next, to sketch an angle of \(270^{\circ}\), keep in mind that angles are measured counter-clockwise from the x-axis for positive angles. Hence, an angle of \(270^{\circ}\) implies that one should draw a line that rotates counter-clockwise from the x-axis and stops at the negative y-axis. Because the full circle is \(360^{\circ}\), an angle of \(270^{\circ}\) will stop at three quarters of full rotation which is on the negative y-axis.
03

Sketch the Angle \(-120^{\circ}\)

Sketching a negative angle means measuring the angle in the clockwise direction from the positive x-axis. So, for a \(-120^{\circ}\) angle, start from the positive x-axis and make a clockwise rotation until you hit the second quadrant or \(-120^{\circ}\) from the positive x-axis. This implies that for a \(-120^{\circ}\) angle, the terminal side (line) will be in the second quadrant of the coordinate system.

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