Transcript Create your proportion!

ANCIENT
GREEKS USED
TRIGONOMETRY
TO MEASURE
THE DISTANCE
TO THE STARS
IN 140 B.C.
HIPPARCHUS
BEGAN TO USE
AND WRITE
TRIGONOMETRY
TRIGONOMETRY
GREEK WORD MEANING:
TRIANGLE
MEASURE
Trigonometry is only used for
RIGHT TRIANGLES
90
RIGHT TRIANGLES MUST HAVE A 90 DEGREE ANGLE
Definitions
• Right Triangle – a triangle with one right angle
and two acute angles.
• Hypotenuse – the longest side in a right triangle.
The hypotenuse is always across from the right
angle.
• Legs – the two other sides in a right triangle that
form an “L” and create the right angle.
• Opposite Side – The side across from the angle
we are talking about.
• Adjacent Side – The side next to the angle we
are talking about.
LEG OPPOSITE TO B
B
LEG ADJACENT TO ANGLE B
Now that we know the pieces of the
right triangle….
Let’s learn about the trigonometric functions.
The Trigonometric Functions
we will be looking at
SINE
COSINE
TANGENT
The Trigonometric Functions are
shortened on the calculator to
the colored part of the word.
SINE
COSINE
TANGENT
SINE
Prounounced
“sign”
COSINE
Prounounced
“co-sign”
TANGENT
Prounounced
“tan-gent”
Greek Letter q
Prounounced
“theta”
Represents an unknown angle
LEG OPPOSITE TO θ
LEG ADJACENT TO θ
θ
SINE OF θ =LENGTH OF LEG OPPOSITE θ
LENGTH OF HYPOTENUSE
COSINE OF θ = LENGTH OF LEG ADJACENT θ
LENGTH OF HYPOTENUSE
TANGENT OF θ = LENGTH OF LEG OPPOSITE θ
LENGTH OF LEG ADJACENT TO θ
We need a way to
remember all of
these ratios…
S
O
H
C
A
H
T
O
A
SOHCAHTOA
Will help us remember
these equations.
Sine
Opposite
Hypotenuse
Cosine
Adjcent
Hypotenuse
Tangent
Opposite
Adjcent
Once Upon there was a mighty Chief SohCahToa.
He fought hard to protect and fix the
damaged tee-pee’s, but they were missing one
side…OH NO!
?
He realized how he could fix his tee-pee’s by
using trigonometry.
SohCahToa
OPP
SIN=
HYP
OPP
TAN=
ADJ
ADJ
COS=
HYP
?
It is all in my name. If I can label the sides of
a triangle I can use that to fix the missing
sides of these tee-pees.
Soh
OPPOSITE THE ANGLE
OPP
SIN=
HYP
X
ADJ
COS=
HYP
X
ADJACENT TO THE ANGLE
Cah
OPPOSITE THE ANGLE
OPP
TAN=
ADJ
X
ADJACENT TO THE ANGLE
Toa
They’re Fixed !!
Thank goodness for Chief SohCahToa.
Opp
sin q 
Hyp
hypotenuse
opposite
opposite
Adj
cos q 
Hyp
q
Opp
tan q 
Adj
adjacent
Finding sin, cos, and tan
Here are some notes and
examples:
When I have a right triangle …
To find the missing side I am going to create a
proportion.
Ex.
1.
2.
3.
4.
5.
sin q o

1
h
Mark the angle that is given.
Label the sides adjacent, opposite and hypotenuse.
Ask myself…what side am I trying to find? What side
am I given?
Which trigonometric function uses those two sides?
Create your proportion.
Let’s Do some examples:
• Copy these onto your blank space under
examples.
Create your proportion!
Opp
Sin q 
Hyp
8
10
4

5
Reduce .
10
Reduce .
3
6

10
5
Create your proportion!
Opposite
Create your proportion!
Adj
Cosq 
Hyp
SOHCAHTOA
Reduce .
Opp 8  4
Tanq 
Adj 6 3
q
Mark the Angle
Adjacent
6
Label the sides…
8
Find the sine, the cosine, and the tangent of angle A.
Give a fraction and decimal answer (round to 4 places).
Create your proportion!
Opposite
9
9
opp

sin A 
hypo 10.8
10.8
 .8333
Create your proportion!
A
Adjacent
6
Mark the Angle
Label the sides…
adj
6
cos A 

hypo 10.8
 .5555
Create your proportion!
opp
tan A 
adj
9

6
 1.5
Find the sine, the cosine, and the tangent of angle A
Adjacent
23.1
Opposite
A
24.5
8.2
Create your proportion!
B
Mark the Angle
Label the sides…
Give a fraction and
decimal answer (round
to 4 decimal places).
opp  8.2
sin A 
 .3347
24
.
5
hyp
Create your proportion!
adj
cos A 
hyp
23.1

24.5  .9429
Create your proportion!
opp
tan A 
adj
8 .2

23.1  .3550
You are done with this part.
• Close out of this screen.
• Put your laptop away (make sure it is
plugged in)
• Come back to your seat and try to
complete the rest of the packet using your
notes and examples.