Basic TrigBasic Trig

Dr. Robert MacKay

Clark College Physics

Introduction Introduction

Right angle trig Sine, cosine, tangent Pathagorean Theorm Inverse tangent

Basic DefinitionsBasic Definitions For a right triangle (90°)

yr

x

yx

Sin =yr

Cos =x

r

Tan =r2 = x2 + y2

=ATAN (y / x)

Y=?V=10m/s

X=?

=40°

Y=6.4 m/s

V=10m/s

X=7.7 m/s

=40°

Sin = YV

Y= VSin 40° = 10m/s(0.643) = 6.43 m/s

Cos =V

X= VCos 40° = 10m/s(0.766) = 7.66 m/s

X

Basic DefinitionsBasic Definitions

Y=?V=?m/s

X=20 m/s

=40°

yx

Sin =yV

Cos =x

V

tan =

1. 25.2 m/s2. 25.9 m/s3. 26.1 m/s4. 26.8 m/s

Y=?V=?m/s

X=20 m/s

=37°

YX

Cos =x

V

tan =

V Cos =x

Cos x V = =

Cos 20m/s

= 26.1 m/s

Y=X tan =20 m/s (.84) =16.8 m/s

a=?

R=?

70°8m

1. 8.62. 8.63. 8.14. 8.55. 8.4

a=1. 2.92. 3.23. 2.84. 2.85. 2.7

a=?

R=20

8m

Sin =820

Cos =a

V

=.4

=sin-1(.4)=23.6°

Basic DefinitionsBasic Definitions

For a right triangle (90°)

yr

x

xr

Sin =yr

Cos =x

r

tan =

Basic DefinitionsBasic Definitions

For a right triangle (90°)

yr

x

xr

Sin =yr

Cos =x

r

tan =

Basic DefinitionsBasic Definitions

For a right triangle (90°)

yr

x

xr

Sin =yr

Cos =x

r

tan =

Vector additionVector addition

Vector addition. The method of adding two vectors to give their resultant effect.

R=A + B

A

B

Vector ComponentsVector Components

Vector components - 2 mutually perpendicular vectors which when added give the original vector

A=Ax+Ay

A

Ax

Ay

Vector CompontsVector Componts East North for a 45° Nof E

Ax=10

Ay=10A=?

Vector CompontsVector Componts

What are the North and east components for a velocity 45° N of E

Ax=?

Ay=?

A=141 m/s

Vectors A and B are at right angles. A has a Vectors A and B are at right angles. A has a magnitude of 20 m/s and B has a magnitude of magnitude of 20 m/s and B has a magnitude of 10 m/s. Find the magnitude of the resultant 10 m/s. Find the magnitude of the resultant

vector A+B.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).

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?

Independence of Vector Independence of Vector ComponentsComponents

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

Vx=10 m/s

Vy=10 m/s

V

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

x Vx,0t 12

axt2

y Vy,0t 12

ayt2

Vx Vx,0 axt

Vy Vy,0 ayt

Independence of Vector Independence of Vector ComponentsComponents

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?

Independence of Vector Independence of Vector ComponentsComponents

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?