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7.4 Trigonometry
Notes
Name:_________________________________
What is Trigonometry?
What is a trigonometric ratio?
The three most common trigonometric ratios are:
Trig Definitions: SOH CAH TOA
Some ways to Remember SOH CAH TOA
Some Old Hillbilly Caught Another Hillbilly Throwing Old Apples
She Offered Her Cat A Heaping Teaspoon of Acid.
Key Concepts of Trigonometric Ratios
What’s Constant?
What Changes?
Steps to Solve Trig Problems:
Step 1: Draw a triangle to fit problem
Step 2: Label sides from angle’s view
- H: hypotenuse
- O: opposite
- A: adjacent
Step 3: Identify trig function to use
- Circle what values you have or are
looking for
- SOH CAH TOA
Step 4: Set up an equation.
Step 5: Solve for variable
Example 1: Find sin L, cos L, tan L, sin N, cos N, and tan N. Express each ratio as a fraction and
as a decimal rounded to nearest hundredth.
Example 2: Find x.
Example 3: Find x.
Check Yourself: Find x. What trig function should you use?
a.
b.
c.
Example 4: EXERCISING A fitness trainer sets the incline on a treadmill to 7°. The walking
surface is 5 feet long. Approximately how many inches did the trainer raise the end of the
treadmill from the floor?
Step 1: Draw a triangle to fit problem
Step 2: Label sides from angle’s view
Step 3: Identify trig function to use
Step 4: Set up equation
Step 5: Solve for variable
Example 5: CONSTRUCTION The bottom of a handicap ramp is 15 feet from the entrance of a
building. If the angle of the ramp is about 4.8°, how high does the ramp rise off the ground to the
nearest inch?
How to Find an Angle: In trigonometry, you can find the measure of the angle by using the
inverse of sine, cosine, and tangent.
Example 6: Find x.
Trig Practice
1) Labels the sides (Opposite – Hypotenuse – Adjacent) from the angle’s point of view
2) Based on the two sides, and the labels you gave them, choose the sine, cosine or tangent ratio
(SOH – CAH – TOA)
3) Set up the equation base on which trig ratio you chose in step 2:
sin(  ) 
O
A
O
, cos( )  , tan( ) 
H
H
A