MATH 150 TEST #1 NAME Chapters 1 – 4 (Form B2-S) (Print) _______________________ ————————————————————————————————————————————– There are 18 questions in this exam (Max 60 points). To receive credit, you must show ALL your work on this exam and your work must justify your answer. NO CREDIT WILL BE GIVEN WHERE NO WORK IS SHOWN. ————————————————————————————————————————————– Problem # 1 – 6: 2 points each
1) Evaluate: sin2 38° + cos2 38° 2) Convert
17𝜋𝜋12
to degrees.
3) Identify the quadrant (or possible quadrants) an angle 𝜃𝜃 that satisfies the given conditions: sec 𝜃𝜃 < 0 , csc 𝜃𝜃 > 0
4) Find the reference angle for −298∘
5) Find the value t to four decimal places in the interval �0, 𝜋𝜋
2� if csc 𝑡𝑡 = 5.487
6) Convert −16.327∘ to degrees, minutes, and seconds to the nearest second.
Problem # 7 – 12: 3 points each
7) The terminal side of an angle 𝜃𝜃 in standard position passes through the point �−2 , √11�.
Find the exact values of sec 𝜃𝜃. (No decimal answer allowed.) Must label the 3 sides of the triangle on the x-y plane to receive credit.
8) Find one solution to the following equation. Assume all angles involved are acute angles.
cot(3𝜃𝜃 − 10∘) = tan(5𝜃𝜃 + 28∘)
9) Find the area of a sector of a circle having radius 𝑟𝑟 = 37.4 ft and central angle 𝜃𝜃 = 185∘.
Answer must include UNITS.
10) Find the linear speed 𝑣𝑣 of the tip of the hour hand of a clock if the hand is 9 cm long. Answer must include UNITS.
11) Find the exact value for tan �−19𝜋𝜋6�. (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.
12) Find the exact value for cot 11𝜋𝜋2
. (No decimal answer allowed.)
Problem # 13 – 18: 5 points each
13) Assume 𝐶𝐶 = 90∘. Solve right triangle 𝐴𝐴𝐴𝐴𝐶𝐶, if 𝑏𝑏 = 24.16 ft and 𝑐𝑐 = 65.37 ft.
14) Radar stations 𝐴𝐴 and 𝐴𝐴 are on an east-west line, 9.4 km apart. Station 𝐴𝐴 detects a plane at 𝐶𝐶, on a bearing of 47∘. Station 𝐴𝐴 simultaneously detects the same plane, on a bearing of 317∘. Find the distance from 𝐴𝐴 to 𝐶𝐶. Answer must include UNITS.
15) From a window 50.0 ft above the street, the angle of elevation to the top of the building across the street is 60.0∘ and the angle of depression to the base of this building is 10.0∘. Find the height of the building across the street. Answer must include UNITS.
16) Graph 𝑦𝑦 = 3sin(2𝑥𝑥 + 𝜋𝜋) − 1 over a two-period interval. Give the following information. Label 5 key points in one period based on this question.
Period: _________ Amplitude: _______ Domain: _________ Range: __________
17) Graph 𝑦𝑦 = −7 sec �𝑥𝑥4� over a one-period interval.
Label vertical asymptotes and 2 key points in the period based on this question.
18) Graph 𝑦𝑦 = 2 cot �𝑥𝑥 − 𝜋𝜋4� over a one-period interval.
Label vertical asymptotes and 3 key points in the period based on this question.
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