1. Basic Trig
Dr. Robert MacKay
Clark College Physics

2. Introduction Right angle trig Sine, cosine, tangent Pathagorean Theorm
Inverse tangent

3. Basic Definitions y r Sin q= y r x Cos q= q r x y Tan q= x
For a right triangle (90°) y r
Sin q= y r x
Cos q= q r x y
Tan q= x
r2 = x2 + y2
q =ATAN (y / x)

4. V=10m/s
Y=?
q=40°
X=?

5. Y
Sin q= V
Y= VSin 40°
= 10m/s(0.643)
= 6.43 m/s
V=10m/s X
Y=6.4 m/s
Cos q= V
q=40°
X= VCos 40°
= 10m/s(0.766)
= 7.66 m/s
X=7.7 m/s

6. Basic Definitions y V=?m/s Sin q= V Y=? x Cos q= q=40° V X=20 m/s y
tan q= x

7. x
Cos q=
V Cos q=x V
20m/s x =
= 26.1 m/s
V =
Cos q
Cos 40°
V=?m/s
Y=? Y
tan q= X
q=37°
Y=X tan 40°
=20 m/s (.84)
=16.8 m/s
X=20 m/s

8. a=? a=
2.9
3.2
2.8
2.7
70° 8m
R=?
8.6
8.1
8.5
8.4

9. a=?
q=? 8m 8
Sin q=
R=20
=.4 20
q=sin-1(.4)=23.6° a
Cos q= V

10. Basic Definitions y Sin q= r r y x Cos q= q r x x tan q= r
For a right triangle (90°) y
Sin q= r r y x
Cos q= q r x x
tan q= r

11. Basic Definitions y Sin q= r r y x Cos q= q r x x tan q= r
For a right triangle (90°) y
Sin q= r r y x
Cos q= q r x x
tan q= r

12. Basic Definitions y Sin q= r r y x Cos q= q r x x tan q= r
For a right triangle (90°) y
Sin q= r r y x
Cos q= q r x x
tan q= r

13. Vector addition
Vector addition. The method of adding two vectors to give their resultant effect. B A
R=A + B

15. Vector Components
Vector components - 2 mutually perpendicular vectors which when added give the original vector
A=Ax+Ay A Ay Ax

29. Vector Componts
East North for a 45° Nof E
A=?
Ay=10
Ax=10

30. Vector Componts
What are the North and east components for a velocity 45° N of E
A=141 m/s
Ay=?
Ax=?

31. Vectors A and B are at right angles
Vectors A and B are at right angles. A has a magnitude of 20 m/s and B has a magnitude of 10 m/s. Find the magnitude of the resultant vector A+B.
For the vectors A and B in the figure above calculate the direction (in degrees) that the resultant vector A+B makes with the x-axis (A direction).

32. Vectors A and B have magnitudes of 18 N and 8 N respectively
Vectors A and B have magnitudes of 18 N and 8 N respectively. They are oriented 45 degrees from each other as shown. What is the magnitude of the resultant vector A+B?

34. Independence of Vector Components
For 2-D projectile motion the vertical and horizontal motions are independent V
Vy=10 m/s
Vx=10 m/s

35. For 2-D projectile motion the vertical and horizontal motions are independent

36. Independence of Vector Components
2-14 A small plane takes off with a constant velocity of 150 km/hr (42 m/s)
at an angle of 37 °. In 3.00 s ,
A) how high is the plane above the ground?
B) What horizontal distance has it traveled?

37. Independence of Vector Components
2-13**
A ball has an initial velocity of 1.3 m/s along the +y direction and starting at to receives an acceleration of 2.10 m/s2 in the +x direction.
A) what is the position of the ball at 2.5 sec after to?
B) What is the velocity of the ball at that time?