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Transcript
We already know so much about Vectors like…
•What is a Vector?
•What is a Scalar?
•What are the parts of a Vector?
•And wait…there’s more
Vector Components
Any vector can be broken up into two perpendicular
components that lie along the x axis and along the y axis.
-You can think of an
individual component of a
vector as the shadow it
would cast on either the x
axis or the y axis.
y component
-We call these the x and
y components of a vector.
x component
y component
also
y component
Components
x component
Island of SOH-CAH-TOA
[Exploring Trigonometric Functions]
SOHCAHTOA Also Means:
“Let’s do Trig!!
But….What is Trigonometry!
Trigonometry, or trig are sets of useful ratios
used for finding various parts of right
triangles.
NOW…”Lets do Trig!”
SOH-CAH-TOA
[SOH]
Sine – Opposite – Hypotenuse
[CAH]
Cosine – Adjacent – Hypotenuse
[TOA]
Tangent – Opposite - Adjacent
First: A quick Geometry
Review
PARTS
OF A
RIGHT
TRIANGLE
O
P
P
O
S
I
T
E
HYPOTENUSE
ADJACENT
So, Sohcahtoa!
[…trans. “Let’s do Trig.!”]
We’ll break it into syllables.
SOH-CAH-TOA
SOH: SINE-OPP-HYP
sin  = opposite side
hypotenuse
O
P
P
O
S
I
T
E
HYPOTENUSE
ADJACENT
CAH-TOA
SOH-
CAH: COSINE-ADJ-HYP
cos  = adjacent side
hypotenuse
O
P
P
O
S
I
T
E
HYPOTENUSE
ADJACENT
TOA
SOH-CAH-
TOA: TAN-OPP-ADJ
tan  = opposite side
adjacent
O
P
P
O
S
I
T
E
HYPOTENUSE
ADJACENT
A QUICK REVIEW
SOH
Sin Opposite Hypotenuse
CAH
Cosine Adjacent Hypotenuse
TOA
Tangent Opposite Adjacent
APPLICATIONS:
Let’s solve a simple problem.
Sohcahtoa!
The natives launch a coconut at 25 m/s at an angle of 30
with the horizontal. What are the horizontal and vertical
components of the velocity?
Vertical component
Y- component
30
Horizontal component
X- component
The solution!
30
Vertical component
Y- component
opposite= sin* hypotenuse
= sin 30 (25 m/s)
= 0.5 (25 m/s) = 12.5 m/s
Horizontal component
X- component
adjacent = cos * hypotenuse
= cos 30 (25 m/s)
= 0.866 (25 m/s) = 21.7 m/s
APPLICATIONS:
Let’s try a WORD problem!
Sohcahtoa!
Find the Height of Mt.
Sohcahtoa
The volcano is rumbling. The
Sohcahtoans need to
sacrifice a Physics
Student. They know the
base of the mountain is 6
Km wide. The angle
formed from the base to
the top is 60°.
How tall is the mountain?
[Use your calculator!!!]
Find the Height of Mt.
Sohcahtoa
What do we know?
=
60°
Base = 6 Km = 3 Km
2
H
e
i
g
h
t
6 Km
What else do know?
sin 
= Opposite side
Hypotenuse
CAH - cos 
= Adjacent side
Hypotenuse
tan 
= Opposite side
Adjacent side
SOH -
TOA -
H
e
i
g
h
t
Which one should we use?
6 Km
WHY??
tan  = Opposite side
Adjacent side
tan 60° =
h _
3 Km
H
e
i
g
h
t
3 Km
h
What if I want to find an
angle?
Here we know the opposite
side and the hypotenuse.
So we will use the sin function
20 cm
Sin-1(opp/hyp) = 

 = 36.87 degrees
- this is called the
inverse sin
function
Back to the Island of SOHCAHTOA

The crafty physics student wants to escape death by
volcano and land behind the angry
SOHCAHTOANS. He builds a slide from the top of
the Volcano (5.2 Km high) to land 7 Km from the
base of the volcano. What are the angles the slide
will make with the volcano and the ground?