1 Radians and arcs / 4 pts
a) Convert \(210^\circ\) to radians. b) Convert \(\dfrac{11\pi}{4}\) to degrees. c) Find the arc length of a sector of radius \(9\text{ in}\) and central angle \(\dfrac{2\pi}{3}\). d) Find the exact area of that sector.
2 Exact values / 4 pts
Give the exact value (no calculator): a) \(\sin\dfrac{5\pi}{3}\) b) \(\cos\dfrac{3\pi}{4}\) c) \(\tan\dfrac{7\pi}{6}\) d) \(\sec\dfrac{11\pi}{6}\) (rationalize).
3 Using the Pythagorean identity / 3 pts
Suppose \(\cos\theta=-\dfrac{8}{17}\) and \(\theta\) is in quadrant III. Find \(\sin\theta\), \(\tan\theta\) and \(\csc\theta\).
4 A ladder (calculator allowed) / 3 pts
A \(4.5\text{ m}\) ladder makes a \(64^\circ\) angle with the ground. Draw a sketch, then find how high the ladder reaches and how far its foot is from the wall, to the nearest hundredth of a meter.
5 Solving an equation / 3 pts
Solve \(2\cos\theta+1=0\) for \(0\le\theta<2\pi\).
6 Wind turbine (calculator allowed) / 3 pts
A wind turbine blade is \(120\text{ ft}\) long and the rotor turns at \(15\) rpm. Find the angular velocity in radians per minute, the speed of the blade tip in feet per minute, and that speed in miles per hour (\(1\text{ mi}=5280\text{ ft}\)), to the nearest tenth.
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