Basic Trig Dr. Robert MacKay Clark College Physics.

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?