1. Trig & Vectors
Unit 2 – Math – Physics

2. Patterns No Pattern Adding? Multiplying? Dividing?
Gives the same number every time
Adding? Multiplying? Dividing?
Patterns

3. A ratio is when we compare two quantities using division.

4. Trig in a Nutshell
Use known ratios to solve for missing pieces of a triangle.

5. Trig Terms
sin = o h
SOH
cos = a
CAH
tan = o a
TOA h o  a

6. Find: Sine, Cosine, & Tangent5
cos = 4
tan = 3 4 5 3  4

7. Steps for Solving Triangles
Label what we know.
Pick a trig function.
Solve with algebra.

8. Make sure your calculator is in degree mode.
WARNING!!!

9. Solve the following Triangle
X = ?
Use TOA
tan = o a
tan 22 = X 17
17 tan 22 =X
X = 6.87
Y = ?
Use CAH
cos = a h
cos 22 = 17 Y
Y cos 22 =17
Y =
cos 22
Y = 18.3 Y X 22 17

10. Solve the following TriangleY 67 X
312

11. Solve the following TriangleY 42 X 83

12. Pythagorean Theorem:
a2 + b2 = c2
Where c = hypotenuse

13. The hypotenuse will be longer than either of the other 2 legs.
The hypotenuse will be Shorter than the sum of the legs.
Hypotenuse Tricks:
Demo here: Where you walk the triangle 5 steps, 5 steps, then ask how long the hypotenuse will be then walk it and count.

14. Inverse Trig Use to solve for  sin = O/H sin-1 sin = sin-1 (O/H)
 = sin-1 (O/H) OR  = arcsin (O/H)
 = cos-1 (A/H)
 = tan-1 (O/A)
How do you get rid of sin? Repent! (sin-1 is the repentance function.  )

15. Solve the following triangle
= ?
cos  = A/H
cos  = 3/5
cos-1cos  = cos-1(3/5)
 = 53.1o 5 Y  3
Now we can solve for Y:
Y= ?
sin  = O/H
sin 53.1 = Y/5
5 sin 53.1 =Y
Y = 3.998

16. Solve the following TriangleX  5 12

17. Solve the following Triangle16 X 22 

18. Basic Vectors
Unit 2 – Physics

19. A scalar is a number.
What is a Scalar?

20. https://www.youtube.co m/watch?v=bOIe0DIMbI 8
What is a Vector?

21. Trig & Vectors What is a Vector? A vector is a number with direction.
(Vectors are drawn as an arrow.)

22. Vector Vocabulary r Y X x-component: horizontal portion (x)
y- component: vertical portion (y)
resultant / magnitude: full vector (r)
direction: angle ()
**Always measure  from the nearest horizontal Reference r Y  X

23. RECTANGULAR FORM NOTATION
X, Y
RECTANGULAR FORM NOTATION

25. Vector examples at the right…
a: b: c: d: e: f:
<2, 5>
<-4, 1>
<5, 0>
Vector examples at the right…
<2, 3>
<3, -3>
<0, 2>

26. [ r, ] & QUADRANT
POLAR FORM NOTATION

27. Q II QI QIII QIV
QUADRANTS

29. Vector examples at the right…
a: b: c: d: e: f:
[3 cm, 70° ] QI
[2.5 cm, 15° ] QII
[3 cm, 0° ] between QI & QIV
Vector examples at the right…
[2 cm, 55° ]QI
[2.5 cm, 45° ] QIV
[1 cm, 90° ] between QI & QII

30. Why are there two forms? WRONG! Rectangular is easier with the math.
Polar is easier to visualize.
<1,2>
+ <5, 7>
<6, 9>
[10,15° ]
+ [20, 40° ]
[30, 55° ]
WRONG!

31. Converting between Rectangular and Polar
**Adding the horizontal and vertical components of a vector does NOT equal the hypotenuse.
TRIG REVIEW: H O  A

32. Converting between Rectangular and Polar
SINE: sin = y/r y = r sin
COSINE: cos = x/r x = r cos
TANGENT: tan  = y/x  = tan-1(y/x)
PYTHAGOREAN:
x2 + y2 = r2
r = √x2 + y2 r y  x

33. Converting between Rectangular and Polar
X = Y=
 =
r =
r cos
r sin
tan-1(y/x)
√x2 + y2

34. Identify what I know.
Pick a formula.
Plug it in.
Solve.
STEPS

35. Applications Resolve this vector: 13 22.6 ° KNOW:  = 22.6° r = 13
FIND:
X = ?
Y = ?
x = r cos = 13 cos 22.6° = 12.0
y = r sin = 13 sin 22.6° = 4.996
<12, 5>