sohcahtoa
September 27, 2013
What's Going On?
White Boards!
sin, cos or tan?
Playing with calculators
Learning Goal ­ I will be comfortable with the three trig ratios (sin, cos and tan)
1
sohcahtoa
September 27, 2013
F.F.M.
Name: _________
Date:_______
Given the right triangle below,
F
identify the opposite, adjacent
and hypotenuse if our reference
angle is F.
T
G
2
sohcahtoa
September 27, 2013
Labelling a Triangle
When we deal with triangles, we need to be able to properly label all
of the sides and all of the angles.
Angles are labelled with capital letters, sides are labelled with lower
case letters. We always label sides based on their OPPOSITE angles.
B
A
C
3
sohcahtoa
September 27, 2013
Reference Angles
When we are exploring right triangles, we typically have what is
called a reference angle.
We use a reference angle so that we can easily talk about different
sides of the triangle without it being confusing.
B
A
C
4
sohcahtoa
September 27, 2013
Reference Angles
Once we have chosen our reference angle we can
refer to the three sides of a right triangle as the:
opposite side
adjacent side
NEW
TERMS!
hypotenuse
5
sohcahtoa
September 27, 2013
The Angle Monster
B
hypotenuse
opposite side
A
C
adjacent side
The angle monster always looks at his opposite side and
hugs his adjacent side and his hypotenuse.
6
sohcahtoa
September 27, 2013
The Angle Monster
B
hypotenuse
adjacent side
A
opposite side
C
The angle monster always looks at his opposite side and
hugs his adjacent side and his hypotenuse.
7
sohcahtoa
September 27, 2013
Reference Angles
G
opposite: ___
adjacent: ___
hypotenuse: ___
H
I
Without a reference angle, we can't do this!!
8
sohcahtoa
September 27, 2013
Reference Angles
G
Reference Angle: ___
opposite: ___
adjacent: ___
hypotenuse: ___
H
I
9
sohcahtoa
September 27, 2013
Reference Angles
Reference Angle: ___
opposite: ___
M
adjacent: ___
hypotenuse: ___
N
O
10
sohcahtoa
September 27, 2013
Reference Angles
Reference Angle: Z
opposite: ___
adjacent: ___
????
X
hypotenuse: ___
Y
Z
NEVER USE THE RIGHT
o
ANGLE (90 ) AS A
REFERENCE ANGLE!!!!
11
sohcahtoa
September 27, 2013
sine (angle) = opposite
hypotenuse
The "sine" of an angle tells you the ratio of the side OPPOSITE the angle to the HYPOTENUSE.
12
sohcahtoa
September 27, 2013
cosine (angle) = adjacent
hypotenuse
The "cosine" of an angle tells you the ratio of the side ADJACENT to the angle to the HYPOTENUSE.
13
sohcahtoa
September 27, 2013
tangent (angle) = opposite
adjacent
The "tangent" of an angle tells you the ratio of the side OPPOSITE the angle to the side ADJACENT to the angle.
14
sohcahtoa
September 27, 2013
The Primary Trigonometric Ratios
sin (angle) = opposite
hypotenuse
soh
cos (angle) = adjacent
hypotenuse
cah
tan (angle) = opposite
adjacent
toa
15
sohcahtoa
September 27, 2013
It's amazing!
YES!!!!
U
O
Y VE
O
L T!
I
hcahto
16
sohcahtoa
September 27, 2013
17
sohcahtoa
September 27, 2013
18
sohcahtoa
September 27, 2013
Take it to the GSP!
19
sohcahtoa
September 27, 2013
Take it to the GSP!
Remember...
sin(angle) is just some number!
sin( ) =
sin( ) =
sin( ) =
sin( ) =
sin( ) =
sin( ) =
sin(any angle) is always ___________
20
sohcahtoa
September 27, 2013
Take it to the GSP!
Remember...
sin(angle) is just some number!
...so is cos(angle)
cos( ) =
cos( ) =
cos( ) =
cos( ) =
cos( ) =
cos( ) =
cos (any angle) is always __________
21
sohcahtoa
September 27, 2013
Take it to the GSP!
Remember...
sin(angle) is just some number!
...so is cos(angle) and tan (angle)
tan( ) =
tan( ) =
tan( ) =
tan( ) =
tan( ) =
tan( ) =
22