May 03, AdvAlg10 3PropertiesOfTrigonometricRatios.notebook. a. sin17 o b. cos 73 o c. sin 65 o d. cos 25 o. sin(a) = cos (90 A) Mar 9 10:08 PM

Transcription

1 a. sin17 o b. cos 73 o c. sin 65 o d. cos 25 o sin(a) = cos (90 A) Mar 9 10:08 PM 1

2 Find another pair of angle measures x and y that illustrates the pattern cos x = sin y. Mar 9 10:11 PM 2

3 If two angles are complementary (add to 90 o ), the sine of one angle equals the cosine of the other. Mar 9 10:12 PM 3

4 Mar 9 10:15 PM 4

5 Mar 9 10:16 PM 5

6 Not interested in finding the angle measure just the sine of the angle or the cosine of the angle The Pythagorean Identity can be used to find the value of the sine of an angle if we are given the cosine of the angle or to find the cosine of an angle if we are given the sine of the angle. Mar 9 10:27 PM 6

7 AND Mar 9 10:32 PM 7

8 from previous page from previous page Mar 9 10:33 PM 8

9 1 60 o shorter leg is half the hypothenuse 1 45 o 30 o 45 o Mar 9 10:36 PM 9

10 Apr 3 12:03 PM 10

11 AdvAlg10 3PropertiesOfTrigonometricRatios.notebook Apr 3 12:03 PM 11

12 Mar 9 10:36 PM 12

13 Mar 9 10:39 PM 13

14 Complements Thm. Mar 9 10:51 PM 14

15 Mar 9 10:59 PM 15

16 The cosine function gets its name from the fact that the cosine of an angle is equal to the sine of the complement of the angle. In addition, the sine of an angle is equal to the cosine of the complement of the angle. Even though the tangent function has been defined as opposite leg over adjacent leg of a right triangle, it is also define as the ratio of the sine of an angle divided by the cosine of the same angle. We should know the exact value of sine, cosine, and tangent for 30 o, 45 o, and 60 o angles. The Pythagorean Identity can be used to find the value of sine of an angle if we are given the cosine of the angle or to find the cosine of an angle if we are given the sine of the angle. Mar 9 11:00 PM 16

17 The cosine function gets its name from the fact that the cosine of an angle is equal to the sine of the complement of the angle. In addition, the sine of an angle is equal to the cosine of the complement of the angle. Even though the tangent function has been defined as opposite leg over adjacent leg of a right triangle, it is also define as the ratio of the sine of an angle divided by the cosine of the same angle. We should know the exact value of sine, cosine, and tangent for 30 o, 45 o, and 60 o angles. The Pythagorean Identity can be used to find the value of sine of an angle if we are given the cosine of the angle or to find the cosine of an angle if we are given the sine of the angle. Mar 9 11:00 PM 17

18 Notes 10-3 Find the length of each leg. Use exact values, no decimals. Use the triangle to complete the table. Use exact values, no decimals. What similarities do you see in the table? Dec 27 3:58 PM 18

19 cos 60 0 = ½ cos 45 0 = 2 2 cos 30 0 = 3 2 cos = sin (90 - ) and the sin = cos ( 90 - ) Dec 27 4:04 PM 19

20 (cos ) 2 + ( sin ) 2 = 1 or ( sin ) 2 + ( cos ) 2 = 1 Dec 27 4:19 PM 20

21 Use the triangles and the lengths of each leg to complete the table below. tan = sin cos Dec 27 4:20 PM 21

22 Practice: 1. Sin 49º = Cos 27º = 2. Cos θ =.187 Find the Sin θ = 3. Cos θ =.956 Sin θ =.292 Find Tan θ Dec 27 4:21 PM 22

23 A Find the exact value of AC and BC. 18 C 30 o B Sep 29 8:49 AM 23

24 Find the exact values of EG and FG. E 5 F G Sep 29 8:52 AM 24

25 Suppose sin θ = 6 5 What is the value of cos θ? What is the value of tan θ? Sep 29 8:58 AM 25

26 10 10 Suppose cos θ = and tan θ = 3, what is the value of sin θ? Sep 29 9:02 AM 26

27 Mar 9 11:07 PM 27

28 Mar 9 11:07 PM 28

29 Mar 9 11:08 PM 29

30 Mar 9 11:08 PM 30

31 Mar 9 11:09 PM 31

32 Mar 21 8:25 AM 32

33 Mar 9 11:09 PM 33

34 Mar 9 11:09 PM 34

35 Mar 9 11:10 PM 35

36 Mar 9 11:11 PM 36

37 Mar 22 8:40 AM 37

38 Mar 9 11:11 PM 38

39 Mar 9 11:12 PM 39

40 Mar 26 7:46 AM 40

41 Mar 9 11:12 PM 41

42 Mar 9 11:12 PM 42

43 x x tan(x) = 1/6 tan 1 (tan(x)) = tan 1 (1/6) x= tan 1 (1/6) o Mar 9 11:12 PM 43

44 Mar 9 11:13 PM 44

45 Mar 9 11:15 PM 45

46 Mar 18 12:35 PM 46

47 Mar 23 7:52 AM 47

48 Mar 18 12:35 PM 48

49 Mar 18 12:35 PM 49

50 Mar 18 12:35 PM 50

51 Mar 18 12:35 PM 51

52 Mar 23 10:14 AM 52

53 Mar 18 12:36 PM 53

54 Apr 4 8:55 AM 54

55 Apr 4 8:56 AM 55

56 Apr 4 8:56 AM 56

57 Apr 5 11:10 AM 57

58 Apr 5 11:09 AM 58

59 Apr 5 11:09 AM 59

60 Apr 5 11:09 AM 60

61 Apr 5 11:09 AM 61

62 Apr 4 8:57 AM 62

63 Apr 4 8:55 AM 63

64 Apr 4 8:53 AM 64