1. Vectors - Finding Vector Components Contents:
Definition of vector components
Whiteboards: Writing the notation
How to find components
Whiteboard Am to VC

2. Vectors - What components are
Y - Component
X - Component

3. Vectors - What components are
Suppose A = 5 cm
Ay = 3 cm
Ax = 4 cm
A = 4 cm x + 3 cm y
(This is how you write it) ^

4. Whiteboards:
Writing the notation
1 | 2 | 3

5. 3.2 m
4.5 m
4.5 m x m y

6. 3.9 m
1.2 m
-1.2 m x m y

7. 4.1 m
1.9 m
-1.9 m x m y

8. Vectors - Finding Components - step by step
Step 1: Find the Trig angle – ACW from x axis
0o Or 360o
90o
180o
270o
27o
This is the trig angle
15o
51o
17o
T = 360 – 17 = 343o OR
T = -17o
T = 270 – 15 = 255o
T = = 321o

9. Whiteboards:
Getting the trig angle
1 | 2 | 3 | 4 | 5 | 6

10. What’s the Trigonometric angle?

11. What’s the Trigonometric angle?

12. What’s the Trigonometric angle?

13. What’s the Trigonometric angle?

14. What’s the Trigonometric angle?

15. What’s the Trigonometric angle?

16. Vectors - Try this yourself
Get out your calculator
type:
sin 90 <ENTER>
1????
If not
<2nd?> MODE
Cursor arrows to “Degree”
<ENTER> <CLEAR>
Try again (sin 90)

17. Vectors - Finding Components - step by step
 = 180o – 27o = 153o
12 m
27o
x = (12 m)Cos(153o) = m
y = (12 m)Sin(153o) = m
Step 2: Figure the sides
using Cos and Sin:
x = mag Cos()
y = mag Sin()
(iff  = trig angle)

18. Vectors - Finding Components - step by step
Step 3: Write it in Vector Component notation:
Vector = -11 m x m y (With sig figs)
Reality Check:
(+ and -),
relative size

19. Vectors - Try this yourself
23.0 m/s
Draw the Components
Figure the components with sin and cos
Write the answer in VC Notation
 = = 121o
23cos(121) x + 23sin(121) y
x y
-11.8 m/s x m/s y

20. Whiteboards:
AM to VC
1 | 2 | 3 | 4 | 5

21. 27.0 km
32.2o
 = 32.2o
27.0cos(32.2) x sin(32.2) y
22.8 km x km y
22.8 km x km y

22. 27o 42 m  = 360 – 27 = 333o 42cos(333) x + 42sin(333) y
37 m x m y
37 m x m y

23. 77o 5.0 feet  = 90 + 77 = 167o 5cos(167) x + 5sin(167) y
-4.9 ft x ft y
-4.9 ft x ft y

24. 38o 110.0 N  = 270 + 38 = 308o 110.0cos(308) x + 110.0sin(308) y
N x N y
68 N x N y

25. 30.0o 5.0 m/s  = 180 + 30.0 = 210.0o 5.0cos(210.0) x + 5.0sin(210) y
-4.3 m/s x m/s y
-4.3 m/s x m/s y