Math 120 Notes 8.2 – Right Triangle Trigonometry
I.
II.
Vocabulary / Identities
A.
What do you know about right triangles?
B.
Give the trig ratios for sin, cos, tan, csc, sec, cot.
C.
How are csc, sec, and cot related to sin, cos, and tan?
Find the values of the trig functions
A.
For each figure, calculate the values of all 6 trig ratios.
1.
III.
IV.
2.
B.
Give another identity for tan.
C.
Given the values of sin and cos, determine the values of the rest of the 6 trig ratios.
1.
sin  
2.
sin  
3
7
, cos  
15
30
3 7
7
, cos  
8
4
Pythagorean Identities
A.
Start with the Pythagorean Theorem and divide by c2. What do you get?
B.
Find the exact value without using a calculator: cos 2 60 
C.
Divide your result from A by cos 2  . Now try sin2  .
D.
Find the exact value without using a calculator: csc 2 47 
1
2
csc 60
cos 2 47
sin2 47
Cofunctions
A.
Do you see a pattern?
1.
2.
B.
a.
sin 2° and the cos 88°
b.
sin 10° and the cos 80°
c.
sin 35° and the cos 55°
A similar relationship holds between tan and cot, sec and csc.
Find the exact value without using a calculator.
1.
C.
On the calculator, find the following (make sure you’re in DEGREE mode!)
cos15
sin 75
Given cot  
1.
tan 
2.
1  cos2 20  cos 2 70
3.
tan(35 ) sec(55 ) cos(35 )
2
, use the trig identities to find the exact value of
5
2.
csc 2 
3.


tan    
2


4.
sec 2 