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Math 150 Test 1 Study Guide

Math 150 Test 1 – Study Guide (Chapter 1 – 4) 1) Evaluate: sin2 124° + cos2 124° 2) Evaluate: sec2 53° – tan2 53° 3) Determine whether each statement is possible or impossible: cos 𝜃𝜃 = − 54.3 4) Convert 105∘20′32′′ to decimal degrees to the nearest thousandth.

5) Convert −19.361∘ 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 132∘.

Answer must include UNITS. 7) Find the area of a sector of a circle having radius 𝑟𝑟 = 17.2 ft and central angle 𝜃𝜃 = 185∘.

Answer must include UNITS.

8) Given latitudes of Los Angeles, 34°N, and Reno, 40°N. Find the distance in kilometers between each pair of cities, assuming they lie on the same north-south line. Use 𝑟𝑟=6400 km for the radius of Earth.

Answer must include UNITS. 9) Find the linear speed 𝑣𝑣 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 𝑣𝑣 of a point on the tread of a tire of radius 18 cm, rotating 35 times per min.

11) Assume 𝐶𝐶 = 90∘. Solve right triangle 𝐴𝐴𝐴𝐴𝐶𝐶, if 𝑏𝑏 = 35.6 ft and 𝑐𝑐 = 61.7 ft. 12) Solve the right triangle ABC with 𝑐𝑐 = 12.7 𝑖𝑖𝑖𝑖, 𝐴𝐴 = 34°30′. Assume C is the right angle. 13) Radar stations 𝐴𝐴 and 𝐴𝐴 are on an east-west line, 5.7 km apart. Station 𝐴𝐴 detects a plane at 𝐶𝐶, on a bearing

of 42∘. Station 𝐴𝐴 simultaneously detects the same plane, on a bearing of 312∘. Find the distance from 𝐴𝐴 to 𝐶𝐶. Answer must include UNITS.

14) A ship leaves port and sails on a bearing of N 47° E for 3.5 hours. It then turns and sails on a bearing of S 43° E for 4 hours. If the ship’s 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 67∘. 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 56.0∘ and the angle of depression to the base of this building is 13.0∘. 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 74.2∘. You then walk back 35 ft. From the second point, the angle of elevation to the top of the building is 51.8∘. Find the height of the building. Answer must include UNITS.

18) Graph 𝑦𝑦 = 4sin(𝑥𝑥 − 𝜋𝜋) + 3 over a two-period interval. Label 5 key points in one period based on the question.

19) Graph 𝑦𝑦 = −5cos(4𝑥𝑥 + 2𝜋𝜋) over a two-period interval. Label 5 key points in one period based on the question.

20) Graph 𝑦𝑦 = −3 csc �𝑥𝑥

2 �. Label vertical asymptotes and 2 key points in the period based on the question.

21) Graph 𝑦𝑦 = 2 sec �𝑥𝑥

6 �. Label vertical asymptotes and 2 key points in the period based on the question.

22) Graph 𝑦𝑦 = −2 cot �2𝑥𝑥 + 𝜋𝜋

4 � Label vertical asymptotes and 3 key points in the period based on the

question.

23) Graph 𝑦𝑦 = 3 tan(3𝑥𝑥 − 𝜋𝜋) Label vertical asymptotes and 3 key points in the period based on the question.

24) Identify the quadrant (or possible quadrants) an angle 𝜃𝜃 that satisfies the given conditions:

tan 𝜃𝜃 < 0 , csc 𝜃𝜃 > 0

25) Find the measure of the supplementary angle of 42°. 26) Use a calculator to find a decimal approximation to five decimal places for cos 74∘35′. 27) Find the value t to four decimal places in the interval �0, 𝜋𝜋

2 � if sec 𝑡𝑡 = 5.0447

28) Convert 23𝜋𝜋 15

to degrees. 29) Convert 105° to radians. 30) Find the exact value of sin 30° − cot 45°. 31) The terminal side of an angle 𝜃𝜃 in standard position passes through the point �−2, −√5�.

Find the exact values of sec 𝜃𝜃. (No decimal answer allowed.) 32) Find the exact values of sin 𝜃𝜃, given that tan 𝜃𝜃 = 7

24 and 𝜃𝜃 is in quadrant III. (No decimal answer allowed.)

33) Find one solution to the following equation.

cot(25° − 3𝜃𝜃) = tan(5𝜃𝜃 + 13∘)

34) Find the reference angle for 562∘ 35) Find the reference angle for − 41𝜋𝜋

3

36) Find the exact value for sec (−180∘). (No decimal answer allowed.)

37) Find the exact value for cot 3𝜋𝜋

2 . (No decimal answer allowed.)

38) Find the exact value for cos(480∘) . (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 �− 17𝜋𝜋 4 �. (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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