Transcript Trigonometry Functions - Wichita State University, Wichita

How to Teach Trig Functions
Sarah Benoit
Planning this Lesson
 Inspiration
• Help organize my thoughts
• Think about what I am wanting to teach
 What is this for…
• Unit/Chapter?
• Section?
Asymptotes
Cotx
Things to
Consider
Reciprocal
Graph
Cosx
Tanx
Opposite/
Adjacent
Period and
Amplitude
Things to
Consider
Graph
Reciprocal
Secx
Adjacent/
Hypotenuse
Trig Functions
Opposite/
Hypotenuse
Sinx
Reciprocal
Cscx
Graph
Things to
Consider
Period and
Amplitude
The Key to Trigonometry
Trigonometric Functions
Things to Know
 Definition
• Relationship between
angles of a triangle
• Ratios of the sides of
the triangle
 How is the angle
represented?
• Theta  
 Trig Names
• Sine  Sin 
• Cosine  Cos 
• Tangent  Tan 
 Reciprocal Names
• Cosecant  Csc 
• Secant  Sec 
• Cotangent  Cot 
Trig Functions
 Sin 
• Opposite/Hypotenuse
O
p
p
o
s
i
t
e
 Cos 
• Adjacent/Hypotenuse
 Tan 
• Opposite/Adjacent
• Sin /Cos 
 Helpful Hint
• SOHCAHTOA

Adjacent
Reciprocals of Trig Functions
 Csc 
• 1/Sin 
• Hypotenuse/Opposite
O
p
p
o
s
i
t
e
 Sec 
• 1/Cos 
• Hypotenuse/Adjacent
 Cot 
• 1/Tan 
• Adjacent/Opposite
• Cos /Sin 

Adjacent
On Your Own…
 Hypotenuse = 5
 Adjacent = 3
 Opposite = 4
 Sin  = ?
 Cos  = ?
5
4
 Tan  = ?

 Csc  = ?
 Sec  = ?
 Cot  = ?
3
Unit Circle
Y
(x,y) /4,Sin
(Cos
,Sin )/4)
/4

X
Unit Circle
(0,1)
(-1/2, √3/2)
/2
2/3
(-√2/2,√2/2)
/3
/4
3/4
(-√3/2, 1/2)
(1/2, √3/2)
/6
5/6
(-1,0) 
(√3/2, 1/2)
0 (1,0)
2
(-√3/2,-1/2) 7/6
11/6 (√3/2,-1/2)
5/4
(-√2/2, -√2/2)
4/3
(-1/2, -√3/2)
(√2/2, √2/2)
7/4
(√2/2,- √2/2)
5/3
3/2
(1/2, - √3/2)
(0, -1)
Graph of Cos  and Sec 
 Things to Consider
• Amplitude?
• Period?
• Y-intercept?
• Asymptotes?
 Differences?
• Between function and
its inverse
 Green Globs
?
Graph of Sin  and Csc 
 Things to Consider
• Period?
• Amplitude?
• Asymptotes?
 Differences?
• Between function and
its inverse
 Green Globs
Cos and Sin Wave
Sine/Cosine Tracer
D. Bennett 3/91
D’
Cos
time
A
D
C
Geometer Sketchpad
Sin
Graph of Tan  and Cot 
 Things to Consider
• Asymptotes?
 Differences?
• Between function and
its inverse
 Green Globs
Tangent on a Circle
Tan
Tangent Tracer
D. Bennett 3/91
D
A
time
C
B
Geometer Sketchpad
Now What…?
 Play Green Globs
• Expert Mode
 What type of
equations should I
use?
• Trig Functions
• Previous forms of
equations you know
What if I still need help?
 Ask for help
 Websites
• http://www.drmath.com/
• http://www.gomath.com/
 Play Green Globs
AND…..
TO BECOME AN EXPERT OF TRIG
FUNCTIONS