Solutions to Exam I Ma120(Blue version), Su05

Trigonometry

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Unformatted text preview: Math 120 Trig Summer 2005 Name: ELMO!” Exam I — Part I No Notes Closed Book No Calculators l. Fill-in the following table with exact values. Note: If a certain entry is undefined, insert “undef.” in the corresponding box. (continues on the back) 2. Fill-in the following table: 1. Convert 15° to radians. EXpress your answer as a multiple of 71'. 057%») = [:9 2. Convert the angle 7, in radians, to degrees. 7:35." (50" «r: (a) fi— 3. Evaluate the following exactly: a. sin[3—:-)+tan(fl) a a! 4— D a b. 25in[—54£]+3tan :3 - E L( c. sec(7r)+csc[—3g-r-) : IL... 4» ,J-—-- = " 2. -—t “l 4. If 7:303:27: and cos€=—-:—, then find cot6. 3 2‘ "*- 1: (0529A- .SI-iaLS =C'v3) *5“ 5 ‘1- “L .. (,4 "‘ S = d: —-— 8 “ a-- '9 5” 77 54». I; g - a ,1: 9 (K fuééww‘k 3 =3” 5‘“ - 5 -3/5 2 6 : ’—— 2 ~4I; 5. Exactly evaluate the following: a. 1 + 1 =(os”7’0'* 519910“ sec2 40° csc2 40° Cgkaauv 555$ = \) sin(—20°) o .. O memormm v —————-— 4— mm") = o 4050—0") OLA/(756L- VMZ>A 3‘a°/ *! I309) .15 L77: - ' fl —[email protected] c. sec[18]cos(18) .. f" (45 /e) 6. Find the following for the graph of y = Zoos x) .a.‘ Amplitude= ’1’ '1‘- Q) / 7. tfl" .. b. Period= g = ’7- ~ 4W (’3) 7. Give an equation for a sine function that has the following characteristics: 0 Amliudeis3 ,_ a .. t o PeriIodtistrr. [:7 ' A o Phasesh1fi1s2 a fizi} Varmé- fl‘fl g) “2:1 L.) 8. If we sweep out an angle 0 6 = 120° in a circle of radius r = 3 meters, then write expressions for a. the length of the subtended arc, and - 2.1V '— 5 = r‘ 6 = 3 ( 3) = b. the area of the corresponding sector A: gin—e: Ill-away = arm” 9. If sin0 < 0 and cos 6 > 0, then. the'angle (9 lies in which quadrant? :II 10. If cos 0 < 0 and tan 0 > 0, then the angle (9 lies' in which quadrant? £171 11. Rapid City has a latitude of 44° 3' (north of the equator). Directly south of Rapid City the Nebraska border has a latitude of 43° (north of the equator). Write an expression for the distance, in miles, from Rapid City to the Nebraska border (“as the crow flies”). Assume that the Earth has a radius of 3,960 miles. 0 7.703lflqu a /°3’='(/+6’35 D=</+i)(%a) 12. Give a formula for the period of y=Atan(cox)+B z" ‘ Explain your reasoning. Note: While this was not specifically discussed in class, you have the tools you need to do this! 13. The graph of g(x), where g(x) = f (x - c), is obtained by shifting the graph off. . . (choose one) to the right by c b. to the left by c c. up by c (1. down by c 14. The graph of g(x), where g(x) = f (x) + c, is obtained by shifting the graph of f . . . (choose one) a. to the right by c b. to the lefi by c @ up by c . down by c 15. Match the graphs below to one of the following functions a. y=—tanx fl' b. =tan x+— y l 2) Choice b c 16. Find functions which match the graphs below. (More than one answer is possible in each case.) 3. Matching Function ecfwéz) Matching Function ,7: PC) (mansw> ...
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