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Chapter 4: Problem 58

Find a positive angle less than \(360^{\circ}\) or \(2 \pi\) that is coterminal with the given angle. $$415^{\circ}$$

Short Answer

Expert verified
The positive angle less than \(360^\circ\) or \(2\pi\) that is coterminal with \(415^\circ\) is \(55^\circ\).

Step by step solution

01

Determine the Given Angle

The given angle is \(415^\circ.\)
02

Identify the Coterminal Angles

Coterminal angles can be found by adding or subtracting \(360^\circ\) or \(2\pi\) radians to the angle. In this case, we subtract \(360^\circ\) because the given angle is more than \(360^\circ\).
03

Subtract \(360^\circ\) from the Given Angle

Subtracting \(360^\circ\) from the given angle, \(415^\circ - 360^\circ = 55^\circ.\)
04

Confirm the Result

55 degrees is less than 360 degrees, so we have reached the solution for the exercise.

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Most popular questions from this chapter

Will help you prepare for the material covered in the next section. a. Graph \(y=\cos x\) for \(0 \leq x \leq \pi\) b. Based on your graph in part (a), does \(y=\cos x\) have an inverse function if the domain is restricted to \([0, \pi] ?\) Explain your answer. c. Determine the angle in the interval \([0, \pi]\) whose cosine is \(-\frac{\sqrt{3}}{2} .\) Identify this information as a point on your graph in part (a).

Graph one period of each function. $$y=\left|2 \cos \frac{x}{2}\right|$$

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

Use a graphing utility to graph two periods of the function. $$y=-2 \cos \left(2 \pi x-\frac{\pi}{2}\right)$$

Write the equation for a cosecant function satisfying the given conditions. $$\text { period: } 3 \pi ; \text { range: }(-\infty,-2] \cup[2, \infty)$$
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