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1) Evaluate: sin2 124Β° + cos 2 124Β°
2) Evaluate: sec2 53Β° β tan2 53Β°
3) Determine whether each statement is possible or impossible: cos ππ = β 54.3
4) Convert 105β20β²32β²β² to decimal degrees to the nearest thousandth.
5) Convert β19.361β to degrees, minutes, and seconds to the nearest second.
6) A circle has radius 15.6 cm. Find the length of the arc intercepted by a central angle of 132β.
Answer must include UNITS.
7) Find the area of a sector of a circle having radius ππ = 17.2 ft and central angle ππ = 185β.
Answer must include UNITS.
8) Given latitudes of Los Angeles, 34Β°N, and Reno, 40Β°N. Find the distance in kilometers between each
pair of cities, assuming they lie on the same north-south line. Use ππ=6400 km for the radius of Earth.
Answer must include UNITS.
9) Find the linear speed π£π£ of the tip of the hour hand of a clock if the hand is 15 cm long.
Answer must include UNITS.
10) Find the linear speed π£π£ of a point on the tread of a tire of radius 18 cm, rotating 35 times per min.
11) Assume πΆπΆ = 90β. Solve right triangle π΄π΄π΄π΄πΆπΆ, if ππ = 35.6 ft and ππ = 61.7 ft.
12) Solve the right triangle ABC with ππ = 12.7 ππππ, π΄π΄ = 34Β°30β². Assume C is the right angle.
13) Radar stations π΄π΄ and π΄π΄ are on an east-west line, 5.7 km apart. Station π΄π΄ detects a plane at πΆπΆ, on a bearing of 42β. Station π΄π΄ simultaneously detects the same plane, on a bearing of 312β. Find the distance from π΄π΄ to πΆπΆ. Answer must include UNITS.
14) A ship leaves port and sails on a bearing of N 47Β° E for 3.5 hours. It then turns and sails on a bearing
of S 43Β° E for 4 hours. If the shipβs rate is 22 knots (nautical miles per hour), find the distance that the
ship is from the port. Round to the nearest whole number.
15) The angle of depression from the top of a building to a point on the ground is 67β. How far is the point on the ground from the top of the building if the building is 194 m high? Answer must include UNITS.
16) From a window 62.0 ft above the street, the angle of elevation to the top of the building across the street is 56.0β and the angle of depression to the base of this building is 13.0β. Find the height of the building across the street. Answer must include UNITS.
17) You need to find the height of a building. From a given point on the ground, you find that the angle of
elevation to the top of the building is 74.2β. You then walk back 35 ft. From the second point, the angle
of elevation to the top of the building is 51.8β. Find the height of the building.
Answer must include UNITS.
18) Graph π¦π¦ = 4sin(π₯π₯ β ππ) + 3 over a two-period interval. Label 5 key points in one period based on the question.
19) Graph π¦π¦ = β5cos(4π₯π₯ + 2ππ) over a two-period interval. Label 5 key points in one period based on the question.
20) Graph π¦π¦ = β3 csc οΏ½ π₯π₯
2οΏ½. Label vertical asymptotes and 2 key points in the period based on the question.
21) Graph π¦π¦ = 2 sec οΏ½π₯π₯
6οΏ½. Label vertical asymptotes and 2 key points in the period based on the question.
22) Graph π¦π¦ = β2 cot οΏ½2π₯π₯ + ππ
4οΏ½ Label vertical asymptotes and 3 key points in the period based on the
question.
23) Graph π¦π¦ = 3 tan(3π₯π₯ β ππ) Label vertical asymptotes and 3 key points in the period based on the
question.
24) Identify the quadrant (or possible quadrants) an angle ππ that satisfies the given conditions:
tan ππ < 0 , csc ππ > 0
25) Find the measure of the supplementary angle of 42Β°.
26) Use a calculator to find a decimal approximation to five decimal places for cos 74β35β².
27) Find the value t to four decimal places in the interval οΏ½0, ππ
2οΏ½ if sec π‘π‘ = 5.0447
28) Convert 23ππ
15 to degrees.
29) Convert 105Β° to radians.
30) Find the exact value of sin 30Β° β cot 45Β°.
31) The terminal side of an angle ππ in standard position passes through the point οΏ½β2, ββ5οΏ½.
Find the exact values of sec ππ. (No decimal answer allowed.)
32) Find the exact values of sin ππ, given that tan ππ = 7
24 and ππ is in quadrant III. (No decimal answer allowed.)
33) Find one solution to the following equation.
cot(25Β° β 3ππ) = tan(5ππ + 13β)
34) Find the reference angle for 562β
35) Find the reference angle for β 41ππ 3
36) Find the exact value for sec (β180β). (No decimal answer allowed.)
37) Find the exact value for cot 3ππ
2 . (No decimal answer allowed.)
38) Find the exact value for cos(480β) . (No decimal answer allowed.)
Must show the reference angle on the x-y plane with the correct labelling on all 3 sides of the
reference triangle to receive credit.
39) Find the exact value for csc 13ππ
6 . (No decimal answer allowed.)
Must show the reference angle on the x-y plane with the correct labelling on all 3 sides of the
reference triangle to receive credit.
40) Find the exact value for tan οΏ½β 17ππ
4 οΏ½. (No decimal answer allowed.)
Must show the reference angle on the x-y plane with the correct labelling on all 3 sides of the
reference triangle to receive credit
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