Download 4.2 Trigonometric Functions of Acute Angles

4.2 Trigonometric Functions of Acute Angles
“As a consequence, progress has come to mean simply more power, more profit, more
productivity, more paper prosperity, all of which are convertible into standards
concerned only with size or magnitude, rather than excellence or quality.”
- Alex Campbell
Objective:

Use special right triangles to establish the six basic trigonometric functions.

Evaluate trig functions with and without a calculator.

Apply right triangle trigonometry to everyday situations.
WARMUP
Do you remember the two special triangles from geometry? You’ve seen these before on the SAT and
ACT also!
Right Triangle Trigonometry
Let’s go ahead and define the six trig functions:
Ex 1:
Complete the table below based on your knowledge of special
right triangles and our newly formed definitions!
Function
30
45
Key -Points:
60
sin 
cos 
tan 
cot 
sec
csc 
Ex 2:
Evaluate the following expressions.
sec 30 cot 45
 
 
3csc    cot  
3
4
Key - Points:
Using One Trig Ratio to find them ALL!
Ex 3: Given sin  
5
, find the values of all six trig functions.
6
Key - Points:
Applying Right Triangle Trig
Ex 4: A right triangle with hypotenuse 8 has one angle of 370.
Find the measures of the other two sides. Also, find the area of the
triangle.
Ex 5: A student standing 220 feet in front of MHS gazes at the
bell tower at an angle of 55 . How tall is the bell tower?
Key - Points: