This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Chapter 6: Applications of Trigonometric Functions
I Section 6.1 RightTriangle Trigonometry A. Trigonometric Functions and Ratios mmonommmc Fatsmzfnom 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.: Wﬁm 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 secsb 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 seceS.= 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" trigonometﬁs function of anzaout'e angle 6 is. egaal'to the cofunction
value of the complementoff};Thiisiisjrue whethera 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 iSrhiéasufed 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 = «aﬁeld93 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—‘Q5 = is.
+On9 0L Bi‘q.‘+° b :3.‘{
+009: 39,4 > C '3 goo C ' \Om
q 5
99: fon'<‘3q 4%) (01.5\ Ham“?
:0
\ ' O
A q 2 g
0 b=3,H 10005 =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 ...
View
Full Document
 Spring '10
 McAveety
 Trigonometry, Ratios

Click to edit the document details