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Chapter 4: Problem 104

Explain the difference between positive and negative angles. What are coterminal angles?

Short Answer

Expert verified
Positive angles are formed from counter-clockwise rotation while negative angles are formed from clockwise rotation. Coterminal angles, on the other hand, are angles that start and end in the same position despite differing by full rotations.

Step by step solution

01

Positive and Negative Angles

The difference between positive and negative angles depends on the direction of rotation. If you imagine a line rotating about the origin on a coordinate plane, a positive angle is formed when the rotation is counter-clockwise, while a negative angle is formed when the rotation is clockwise.
02

Coterminal Angles

Coterminal angles are angles that share the same initial and terminal sides. In other words, if you start at the same position for two angles and end in the same position, the angles are coterminal. They might look different because of multiple revolutions, but in terms of rotation they end up in the same place. For instance, the angles \(0^{\circ}\), \(360^{\circ}\), and \(-360^{\circ}\) are all coterminal because they start and end at the same place, despite differing by full rotations.

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Most popular questions from this chapter

Determine whether each statement makes sense or does not make sense, and explain your reasoning. I made an error because the angle I drew in standard position exceeded a straight angle.

Use a graphing utility to graph each function. Use a viewing rectangle that shows the graph for at least two periods. $$y=\cot 2 x$$

Graph \(y=\sin \frac{1}{x}\) in a [-0.2,0.2,0.01] by [-1.2,1.2,0.01] viewing rectangle. What is happening as \(x\) approaches 0 from the left or the right? Explain this behavior.

will help you prepare for the material covered in the next section. a. Graph \(y=-3 \cos \frac{x}{2}\) for \(-\pi \leq x \leq 5 \pi\) b. Consider the reciprocal function of \(y=-3 \cos \frac{x}{2}\) namely, \(y=-3 \sec \frac{x}{2} .\) What does your graph from part (a) indicate about this reciprocal function for \(x=-\pi, \pi, 3 \pi,\) and \(5 \pi ?\)

Use a vertical shift to graph one period of the function. $$y=\cos x+3$$
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