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MATH REVIEWER:
I. Convert the following angles:
1. -720° to revolution (-2 revolution)
2. to degrees-minutes-seconds (134°55’01”)
3. 21.56° to radians (0.3763rad)
II. Name three angles (two positive, one negative) that are coterminal with the given angle.
1. 40° (400°, 760°, -320°)
2. -62° (298°, 658°, -422°)
III. Identify the reference angle of the following:
1. (75° or or )
2. revolution (72° or or )
IV. Solve the following Triangle PQR
1. ÐP = 32.6°, ÐR = 46.9°, r = 115 (ÐQ = 100.5°, q = 155, p = 84.9)
2. ÐP = 54.2°, ÐQ = 45.9°, r = 76.1 (ÐR = 79.9°, q = 55.5, p = 62.7)
3. ÐQ = 113.4°, ÐP = 27.5°, p = 56.3 (ÐR = 39.1°, r = 76.9 p = 112)
V. Solve the following word problems:
1. Find the angular velocity in radians per second of the minute hand of a clock. Express the answer in terms of p.
2. Calculate the angular velocity in radians per minute of a Ferris wheel 315 ft in diameter that takes 48 s to rotate once. Express the answer in terms of p (0.00069prad/min).
3. If you sat on the rim of the Ferris wheel in number 4, what would your linear velocity be, to the nearest foot per minute?(0.34ft/min)
4. At a particular instant, when an airplane was directly above a straight line road connecting two small towns, the angle of depression of these towns were 10.2° and 8.7°. Find the straight-line distances from the airplane to each of the towns at this instant given that the towns are 8.45km apart and determine the height of the airplane at this instant. (4.6km, 3.9km, 0.76km)
5. A ladder 35.4 ft long is leaning against an embankment inclined 62.5° to the horizontal. If the bottom of the ladder is 10.2ft from the embankment, what is the distance form the top of the ladder down the embankment to the ground? (29.5ft)