Survey

* Your assessment is very important for improving the work of artificial intelligence, which forms the content of this project

Document related concepts

Integer triangle wikipedia, lookup

Relativistic angular momentum wikipedia, lookup

Tensors in curvilinear coordinates wikipedia, lookup

Metric tensor wikipedia, lookup

Cartesian tensor wikipedia, lookup

Riemannian connection on a surface wikipedia, lookup

Covariance and contravariance of vectors wikipedia, lookup

History of trigonometry wikipedia, lookup

Pythagorean theorem wikipedia, lookup

Trigonometric functions wikipedia, lookup

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
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]
[TOA]
First: A quick Geometry
Review
PARTS
OF A
RIGHT
TRIANGLE
O
P
P
O
S
I
T
E
HYPOTENUSE
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
CAH-TOA
SOH-
hypotenuse
O
P
P
O
S
I
T
E
HYPOTENUSE
TOA
SOH-CAH-
tan  = opposite side
O
P
P
O
S
I
T
E
HYPOTENUSE
A QUICK REVIEW
SOH
Sin Opposite Hypotenuse
CAH
TOA
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
= 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?
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 
Hypotenuse
tan 
= Opposite side
SOH -
TOA -
H
e
i
g
h
t
Which one should we use?
6 Km
WHY??
tan  = Opposite 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?
```
Related documents