1. Bell Ringer ( 5 mins in notebook)
Find his horizontal velocity? X

2. Bell ringer
Find his horizontal velocity?

3. Lesson Objectives
We will analyze motion in 2 Dimensions using vectors & trigonometry
I will use trigonometry to analyze motion in 2 Dimensions by finding the direction (sides) and the angle.
DQ: How do I find 1 side when I have 2 sides? How do I solve for the missing angle when I have 2 sides ?How do I solve for 1 missing side when I have the angle and 1 other side?

4. AGENDA Review- Pythagorean theorem & Triangles Intro to Trig functions
Worksheet: Using calculator
Worksheet: Solving with trig
Physics Application problems

5. Makiah &Christiana- October 17th!!!

6. Callie Handy’s October 19th!!!

7. BUT……what about the direction?
since it is a VECTOR we should include a DIRECTION on our final answer. N
W of N
E of N
N of E
N of W W E
N of E
S of W
S of E
NOTE: When drawing a right triangle that conveys some type of motion, you MUST draw your components HEAD TO TOE.
W of S
E of S S

8. BUT…..what about the VALUE of the angle???
Just putting North of East on the answer is NOT specific enough for the direction. We MUST find the VALUE of the angle.
To find the value of the angle we use a Trig function called TANGENT.
109.8 km
55 km, N q
N of E
95 km,E
So the COMPLETE final answer is : km, 30 degrees North of East

9. Trig functions Represent the ratio of 2 sides of a triangle
Has special names
Helps find a missing side or angle of a right triangle

10. Trigonometry
Obj: I can to use trigonometry to find unknown sides and unknown angles in a triangle.
Trigonometry is concerned with the connection between the sides and angles in any right angled triangle.
Angle

11. The sides of a right -angled triangle are given special names:
The hypotenuse, the opposite and the adjacent.
The hypotenuse is the longest side and is always opposite the right angle.
The opposite and adjacent sides refer to another angle, other than the 90o. A

12. The Trigonometric Functions we will be looking at
SINE
COSINE
TANGENT

13. The Trigonometric Functions
SINE
COSINE
TANGENT

14. SINE
Prounounced “sign”

15. Prounounced “co-sign”
COSINE
Prounounced “co-sign”

16. Prounounced “tan-gent”

17. Represents an unknown angle
Greek Letter q
Prounounced “theta”
Represents an unknown angle

18. hypotenuse
hypotenuse
opposite
opposite
adjacent
adjacent

19. We need a way to remember all of these ratios…

20. Some
Old
Hippie
Came A
Hoppin’
Through
Our
Old Hippie
Apartment

21. Sin
SOHCAHTOA
Opp
Hyp
Cos
Adj
Hyp
Tan
Opp
Adj
Old Hippie

22. Using trigonometry on the calculator
All individual angles have different sine, cosine and tangent ratios (or decimal values).
Scientific calculators store information about every angle.
We need to be able to access this information in the correct manner.

23. Finding the ratios
The simplest form of question is finding the decimal value of the ratio of a given angle.
Find:
sin 32 =
sin 32 =
0.5514

24. Finding a side from a triangle
To find a missing side from a right-angled triangle we need to know one angle and one other side.
Note: If
Cos45 =
To leave x on its own we need to move the ÷ 13.
It becomes a “times” when it moves.
Cos45 x 13 = x

25. Finding a side from a triangle
There are occasions when the unknown letter is on the bottom of the fraction after substituting.
Cos45 =
Move the u term to the other side.
It becomes a “times” when it moves.
Cos45 x u = 13
To leave u on its own, move the cos 45 to other side, it becomes a divide.
u =

26. When the unknown letter is on the bottom of the fraction we can simply swap it with the trig (sin A, cos A, or tan A) value.
Cos45 =
u =

27. 7 cm k
30o 4.
We have been given the adj and hyp so we use COSINE:
Cos A = H A
Cos A =
Cos 30 =
Cos 30 x 7 = k
6.1 cm = k

28. 4 cm r
50o 5.
We have been given the opp and adj so we use TAN:
Tan A = A O
Tan A =
Tan 50 =
Tan 50 x 4 = r
4.8 cm = r

29. 12 cm k
25o 6.
We have been given the opp and hyp so we use SINE:
Sin A = H O
sin A =
sin 25 =
Sin 25 x 12 = k
5.1 cm = k

30. Practice

31. x
5 cm
30o 7.
Cos A = H
Cos 30 =
x = A
x = cm
sin A = m
8 cm
25o 8. H
sin 25 = O
m =
m = cm

32. sin 30 = 0.5
cos 30 = 0.866
tan 30 =
sin 50 = 0.766
cos 50 =
tan 50 =

33. Using ratios to find angles
We have just found that a scientific calculator holds the ratio information for sine (sin), cosine (cos) and tangent (tan) for all angles.
It can also be used in reverse, finding an angle from a ratio.
To do this we use the sin-1, cos-1 and tan-1 function keys.

34. ( ) ( ) Example: sin x = 0.1115 find angle x. sin-1 0.1115 = shift sin
x = 6.4o
2. cos x = find angle x
cos-1
0.8988 =
shift
cos ( )
x = cos-1 (0.8988)
x = 26o

35. Finding an angle from a triangle
To find a missing angle from a right-angled triangle we need to know two of the sides of the triangle.
We can then choose the appropriate ratio, sin, cos or tan and use the calculator to identify the angle from the decimal value of the ratio.
14 cm
6 cm C 1.
Find angle C
Identify/label the names of the sides.
b) Choose the ratio that contains BOTH of the letters.

36. 14 cm
6 cm C 1.
We have been given the adjacent and hypotenuse so we use COSINE:
Cos A = H A
Cos A =
Cos C =
Cos C =
C = cos-1 (0.4286)
C = 64.6o

37. Find angle x 2.
8 cm
3 cm x
Given adj and opp
need to use tan:
Tan A = A O
Tan A =
Tan x =
Tan x =
x = tan-1 (2.6667)
x = 69.4o

38. 3.
12 cm
10 cm y
Given opp and hyp
need to use sin:
Sin A =
sin A =
sin x =
sin x =
x = sin-1 (0.8333)
x = 56.4o

39. Summary
To find 1 side when I have 2 sides of a right triangle and I will use________ ________.
To solve for the missing angle when I have 2 sides I can use the _________ trig function.
To solve for 1 missing side when I have the angle and 1 other side I can use_________.

40. Summary
To find 1 side when I have 2 sides of a right triangle and I will use________ ________.
To solve for the missing angle when I have 2 sides I can use the _________ trig function.
To solve for 1 missing side when I have the angle and 1 other side I can use_________.
Pythagorean theorem

41. Summary
To find 1 side when I have 2 sides of a right triangle and I will use________ ________.
To solve for the missing angle when I have 2 sides I can use the _________ trig function.
To solve for 1 missing side when I have the angle and 1 other side I can use_________.
Pythagorean theorem
Inverse

42. Summary
To find 1 side when I have 2 sides of a right triangle and I will use________ ________.
To solve for the missing angle when I have 2 sides I can use the _________ trig function.
To solve for 1 missing side when I have the angle and 1 other side I can use_________.
Pythagorean theorem
Inverse
trig functions
( SOH CAH TOA)