WARM UPWARM UP

Find the following missing values.Find the following missing values.

1)1) 2)2)

35

z

w

200

zw

160

3045

Section 8.6Section 8.6

Sine and Cosine Sine and Cosine RatiosRatios

Three Trig. RatiosThree Trig. Ratios

1)1) sinesine2)2) cosinecosine3)3) tangenttangent

Today we are looking at the Today we are looking at the

Sine and CosineSine and Cosine

sine ratiosine ratioleg opposite of opp

sine of ; sin hypotenuse hyp

AA A

A

BCLeg opposite

Hypotenuse

cosine ratioscosine ratiosleg adjacent of adj

cosine of ; cos hypotenuse hyp

AA A

A

BC

Leg adjacent

Hypotenuse

13

5

x

X

Y

b

1.1. Find Find cos Xcos X

2.2. Find Find sin Xsin X

3.3. Find Find cos Ycos Y

4.4. Find Find sin Ysin Y

12

13

We must first find “b”.It’s a Pythagorean Triple! So b = 12

b =

1

25

135

13

12

13

Calculator StuffCalculator Stuff

MAKE SURE YOU ARE MAKE SURE YOU ARE IN IN DEGREEDEGREE MODEMODE EVERY EVERY TIME!!!!!!!!!!!!!!TIME!!!!!!!!!!!!!!

Calculator StuffCalculator StuffFind the missing values.Find the missing values.

5) sin 345) sin 34oo==

6) cos 896) cos 89oo==

7) sin 7) sin ? ? oo = 0.1510 = 0.1510

8) cos 8) cos ? ? oo = .5592 = .5592

0.5591929

0.0174524

Use sin-1 on calc8.68488o

Use cos-1 on calc55.9995o

z

28

y

1000

x

o

9) Find the measure of the missing angles and 9) Find the measure of the missing angles and lengths.lengths.

cos 621000

x

z = 180 – 90 – 28 = 62o

62o

cos62 1000 10001000

x

469.472 x

469

You can use TRIG or PYTHA. THM to find “y”

2 2 2469 1000y 2 2 21000 469y 2 780,039y

2 780,039

883.198

y

y

883

HINT: It is easiest to find the missing value that has two known values…….. In this case find “z” first since you already know two sides.

Find the Find the missing valuesmissing values..10) 10) 2 2 218 30z

z

y

x

1830

2 2 230 18 576z 2 576z

576 24z

24

24cos

30x

1 24cos 36.8699

30

37

o

ox

37o

180- 90 – 37 =

53o53o

Drop the Altitude from the vertex angle B and make two right triangles. Now you can use trig to find the missing angles.

4

55

B

A C

Find the measures of all three Find the measures of all three anglesangles..

2cos

5A

1 2cos

5

1 2cos 66.422

5

66o m A

This is a great problem! Can be very tricky!!!

2 266o 66o

180 – 66 – 66 = 48o

48o

LADDERSLADDERS!!12) A 6 12) A 6 mm ladder reaches ladder reaches

higher up a wall when placed higher up a wall when placed at a 70 degree angle than at a 70 degree angle than when placed at a 60 degree when placed at a 60 degree angle.angle.

How much higher, to the How much higher, to the nearest tenth of a meter?nearest tenth of a meter?

LADDERSLADDERS!!12) A 6 m ladder reaches higher up a wall when placed at a 70 12) A 6 m ladder reaches higher up a wall when placed at a 70

degree angle than when placed at a 60 degree angle.degree angle than when placed at a 60 degree angle.

How much higher, to the nearest tenth of a meter?How much higher, to the nearest tenth of a meter?

70o60o60o6

feet

70o

6 f

eet

LADDERSLADDERS!!12) A 6 m ladder reaches higher up a wall when placed at a 70 degree 12) A 6 m ladder reaches higher up a wall when placed at a 70 degree

angle than when placed at a 60 degree angle.angle than when placed at a 60 degree angle.

How much higher, to the nearest tenth of a meter?How much higher, to the nearest tenth of a meter?

sin 606

y

70o60o

60o

6 fe

et

70o

6 f

eet

xy

sin 706

x0.866

6

y 0.9397

6

x

5.196 ft y 5.6382 ft x

5.6382 – 5.196 = 0.4422 = 0.4 ft

PRACTICEPRACTICE

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