1.
The London Eye, the world’s largest Ferris wheel, completes one revolution every 30 minutes. By how many degrees will it rotate in 1 minute?
Chapter 4: Trig Functions
Problems: # 4, 6, 14, 26, 30, 34, 36, 42, 52, 58, 62
The London Eye, the world’s largest Ferris wheel, completes one revolution every 30 minutes. By how many degrees will it rotate in 1 minute?
The London Eye in Problem 1 has 32 cabins evenly spaced along the wheel. If the cabins are numbered consecutively from 1 to 32, what is the angular separation between cabins number 1 and number 15?
For Problems 3–4, find two angles, one positive and one negative, that are coterminal with the given angle.
For the angles in Problems 5–6, state the corresponding quadrant and reference angle. Give three other angles with the same reference angle, one for each of the other three quadrants. Sketch all four angles.
Let [latex]\widetilde{\theta} = f(\theta)[/latex] be the function that gives the reference angle of [latex]\theta{.}[/latex] For example, [latex]f(110°) = 70°[/latex] because the reference angle for [latex]110°[/latex] is [latex]70°{.}[/latex]
| [latex]\theta[/latex] | [latex]0°[/latex] | [latex]30°[/latex] | [latex]60°[/latex] | [latex]90°[/latex] | [latex]120°[/latex] | [latex]150°[/latex] | [latex]180°[/latex] | [latex]210°[/latex] | [latex]240°[/latex] | [latex]270°[/latex] | [latex]300°[/latex] | [latex]330°[/latex] | [latex]360°[/latex] |
| [latex]f(\theta)[/latex] | [latex]\hphantom{000}[/latex] | [latex]\hphantom{000}[/latex] | [latex]\hphantom{000}[/latex] | [latex]\hphantom{000}[/latex] | [latex]\hphantom{000}[/latex] | [latex]\hphantom{000}[/latex] | [latex]\hphantom{000}[/latex] | [latex]\hphantom{000}[/latex] | [latex]\hphantom{000}[/latex] | [latex]\hphantom{000}[/latex] | [latex]\hphantom{000}[/latex] | [latex]\hphantom{000}[/latex] | [latex]\hphantom{000}[/latex] |
Let [latex]\widetilde{\theta} = f(\theta)[/latex] be the function that gives the reference angle of [latex]\theta{.}[/latex] (See Problem 7.) Is [latex]f[/latex] a periodic function? If so, give its period, midline, and amplitude. If not, explain why not.
For Problems 9–20, solve the equation exactly for [latex]0° \le \theta \le 360°{.}[/latex]
[latex]\sin \theta = \dfrac{-1}{2}[/latex]
[latex]\cos \theta = \dfrac{-1}{\sqrt{2}}[/latex]
[latex]2\cos \theta + 1 = 0[/latex]
[latex]5\sin \theta + 5 = 0[/latex]
[latex]\tan \theta - 1 = 0[/latex]
[latex]\sqrt{3} + 3\tan \theta = 0[/latex]
[latex]\cos \theta = \cos(-23°)[/latex]
[latex]\sin \theta = \sin(370°)[/latex]
[latex]\tan \theta = \tan 432°[/latex]
[latex]\tan \theta = \tan (-6°)[/latex]
[latex]\sin \theta + \sin 83° = 0[/latex]
[latex]\cos \theta + \cos 429° = 0[/latex]
For Problems 21–26, solve the equation for [latex]0° \le \theta \le 360°{.}[/latex] Round your answers to two decimal places.
[latex]3\sin \theta + 2 = 0[/latex]
[latex]5\cos \theta + 4 = 0[/latex]
[latex]\dfrac{2}{3}\tan \theta + 1 = 0[/latex]
[latex]-4\tan \theta + 12 = 0[/latex]
[latex]4