Download Notes Intro to Trigonometry Day 1

Notes Intro to Trigonometry
Day 1
Measurement
Triangle Trigonometry means _________________ _______________________. Trig. involves ratios that compare 2 sides of a triangle. (“ratio” means fraction)
Right
Trigonometry only applies to __________ triangles (triangles that have a right angle)
When we use trig, we are interested in figuring out how long a side is or how big an angle is without measuring it. To learn the procedure, we have to know a few vocabulary words:
Hypotenuse: The side across from the right angle.
Angle of reference (or angle of interest):
"Starting Point" of every problem.
Opposite side:
The side across from the angle of interest.
Adjacent side: The side next to the angle of interest, but not the hypotenuse.
Let’s practice.
Using the marked angle as the angle of interest, label the hypotenuse, opposite and adjacent sides. F
X
)
C
A
)
Y
Z
B
D
)
E
Now, the ratios: There are 3 trigonometric rations that you need to memorize. They have funny names:
The sine ratio is this: sine <X = opposite
hypotenuse
SOH
The cosine ratio: cosine <X = adjacent
hypotenuse
CAH
The tangent ratio: tangent <X = opposite
adjacent
TOA
SOH­CAH­TOA
Let’s practice:
SOH­CAH­TOA
Fill in the ratio for the requested angle of reference. Would it help to label all the sides first?
R
C
12
13
B
5
A
N
7
P
24
x
9
25
M
S
m
T
sin <C = _____
sin <M = _____
sin <R = _____
cos <C = _____ cos <M = _____
cos <R = _____
tan <C = _____
tan <M = _____
tan <R = _____
Use your calculator to find the: sin 41° = cos 12° = tan 3° = (Round to 3 places)
1. Given the following triangle, find the missing side:
16
)
20o
x
Always ask yourself, "From the angle of interest, what sides do I have? Opposite, Adjacent, or Hypotenuse?"
Your answer will lead you to the correct ratio to use.
In this case, we have the ______________ and the _______________ side. That means we use the _______ ratio. Here's the set up:
Find the value for the angle, substitute, and then cross multiply and solve for the variable.
(Round to 1 decimal)
(Round to 1 decimal)
2. Find the measure of the missing sides.
80
m
SOH­CAH­TOA
o
10
p
3. Find the missing sides:
t
r
)42
o
25
SOH­CAH­TOA
SOH­CAH­TOA
s
4.
m
120
o
)
65
5.
)
24
75
t
o
w
SOH­CAH­TOA
Assign#_______
Worksheet 9.6