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Chapter 4: Problem 27

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

Short Answer

Expert verified
In standard position, a \(270^{\circ}\) angle ends on the negative y-axis after doing three quarters of a complete revolution counter-clockwise. In contrast, a \(120^{\circ}\) angle only does a third of a complete revolution counter-clockwise, ending somewhere in the second quadrant.

Step by step solution

01

Plotting the \(270^{\circ}\) angle

Start by drawing a pair of perpendicular lines that intersect at a point. This represents the x and y axes. Since we are sketching a \(270^{\circ}\) angle in standard position, it starts from the positive x-axis and moves counter-clockwise. You will do 3 quarters of a full revolution around the origin (as \(270^{\circ}\) is 3/4 of \(360^{\circ}\)) and end on the negative y-axis.
02

Sketching the \(120^{\circ}\) angle

To sketch the \(120^{\circ}\) angle, again start from the positive x-axis. But this time, you will do a third of a full revolution around the origin (since \(120^{\circ}\) is 1/3 of \(360^{\circ}\)) and end somewhere in the second quadrant.

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