Completed_6.1S16.pdf - Chapter 6 Applications of...

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Unformatted text preview: Chapter 6: Applications of Trigonometric Functions I Section 6.1 Right-Triangle Trigonometry A. Trigonometric Functions and Ratios mmonommmc Fats-mzfnom OF AN ANGLE a m A- mrsm TRIANGLE apposite . hypotenuse sm0=m~r=z --._.__._.__.__. -' csc. 9 3 a, hypotenuse cc" opposite b , . . hypotenuse. g "71 sec 0.: Wfi-m 7 adjacent. 7 £059 = W . hyyotenuse 6 adjacent b opyosit’e,‘ :aéijacentw E (I moms: 1’ opponte c c“ = mam? 0‘ c‘=q +'1 CLQHU it M A yr». Q‘E b=fi >7C =L‘. Ci Ex. 1: Find the exact values for the six trigonometric functions of the angle 6 above. =|-_\_.‘~\~Fi ” 7 sme=g=g=i csce=%_“-*- h c q 3 -9. cose=§=fl secs-b W ’- L1 +0519" 3 7.. J.— CO+9=£ «H " 3 EX. 2: Find the other five trigonometric function values of 6, given that 6 is an acute angle of a right triangle with sin 9 = E. 5 3m 9 3 2‘. : Q. 5 C 2 a _ a (23 +b — (5) b=\’2\ csce=£'§- 0L 2 baht J'- a=2 “”9: 35- sece-S.= 5. mm . B. Compliments 6 2‘ CO“ 9 _ 1‘ ' b [m .,,. V that at: 5:12 mm? ”gum it: $1343}; 1' ' G- 2 The value of any" trigonome-tfis function of anzaout'e angle 6 is. egaal'to the cofunction value of the complementoff};Thiisiisjrue whether-a ismcasared in; degrees or in radians; " 0 in degrees. :sinH =- 603(90“ —-> 6) gas a = gm (we 6’) tan é 2.00160" - 6) mtg: tanQQQOf’? — 6’) w ‘ 3608 m 050(790" ——~ 6) ngf} m see(90°‘z— 6}) If as iSr-hiéasufed in radians; replace- 90° with 35 2; EX. 3: a. Given that est—68234040, find tan 22° ton 22° = cofiqd— 22W = c0* 68" mu 9 = «afield-93 b. Given that cos 72° 2,5 0.3090, find sin 18°. sun \‘8” = no: (fio°—\‘8°) = C05 “2° = C. Solving Right Triangles A = 25° Q' - ’2 .21- 0 Ex. 4: Solve right triangle ABC ifA = 23° and c = 5.8. B "" (0'1 b '- 5 ' 3H 8 SWWAI= .0; A p C LA +AB+ LC =\8D° C . SWWA : a 250*L5 “30° =\%O° 5.2 sxn23°_=a LB+\\3°=\30° 2.21 45‘5“: C2 A a *b C. b (7 7:43 :b" =C5$3 ' ‘ 5.\52q +\o’*‘= 52>. (0‘4 . b = 5355:? 1 5‘3“ Ex. 5: Solve right triangle ABC if a = 9.5 and b = 3.4. A:"{O,5O CLT—‘Q-5 = is. +On9 0L Bi‘q.‘+° b :3.‘-{ +009: 39,4 > C '3 goo C ' \O-m q 5 99: fon'<‘3q 4%) (01.5\ Ham“? :0 \ ' O A q 2 g 0 b=3,H 1-0005 =11 50 D. Applications Angle of Elevation Angle of Depression Ex. 6: To determine the height of a cloud at night, a farmer shines a spotlight straight upward to a spot on the cloud. The angle of elevation to this same spot on the cloud from a point located 150 feet horizontally from the spotlight is 682°. Find the height of the cloud. )4. 68 \50’657 +051 (93.20 3 35— 150 ...
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