Download graphs of the six trigonometric functions and their properties

Survey
yes no Was this document useful for you?
   Thank you for your participation!

* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project

page
1
page
2
page
3
page
4
Document related concepts
no text concepts found
Transcript 
GRAPHS OF THE SIX TRIGONOMETRIC FUNCTIONS AND THEIR PROPERTIES
I. The graph of y = sin x
x
y = sin x (x,y)
0
π/6
π/2
5π/6
π
7π/6
3π/2
11π/6
2π
Properties of the sine function:
1. Domain _________________
2. Range _________________
3. Symmetry _______________
4. Type of Function __________
5. x-intercepts __________________
6. y-intercepts __________________
7. Maximum Values ____________
8. Minimum Values ____________
9. Period __________
II. The graph of y = cos x
x
y = cos x (x,y)
0
π/3
π/2
2π/3
π
4π/3
3π/2
5π/3
2π
1
Properties of the cosine function:
1. Domain _________________
2. Range _________________
3. Symmetry _______________
4. Type of Function __________
5. x-intercepts __________________
6. y-intercepts __________________
7. Maximum Values ____________
8. Minimum Values ____________
9. Period __________
III. The graph of y = csc x
Properties of the cosecant function:
1. Domain _________________
2. Range _________________
3. Symmetry _______________
4. Type of Function __________
5. x-intercepts __________________
6. y-intercepts __________________
7. Maximum Values ____________
8. Minimum Values ____________
9. Period __________
IV. The graph of y = sec x
2
Properties of the secant function:
1. Domain _________________
2. Range _________________
3. Symmetry _______________
4. Type of Function __________
5. x-intercepts __________________
6. y-intercepts __________________
7. Maximum Values ____________
8. Minimum Values ____________
9. Period __________
Transformations on the Graphs of the Sine, Cosine, Secant and Cosecant Functions
y = a fnct b (x + c) + d
a (amplitude) – | a |, creates a vertical compression or stretch
Ex. y = 2 sin x
b (period) – change in period, 2 π / | b |, creates a horizontal
compression or stretch
Ex. y = ½ sin 4 x
c creates a horizontal shift to the right or left
Ex. y = 4 cos (x – π/3)
d creates a vertical translation up or down
Ex. y = ¼ cos (x + π) - 2
Note: When a negative appears in front of the a, then the function is reflected about the
x-axis.
Ex. y = - cos 2 x + ½
V. The graph y = tan x
x
y = tan x (x,y)
-π/3
-π/4
-π/6
0
π/6
π/4
π/3
Properties of the tangent function:
1. Domain _________________
2. Range _________________
3. Symmetry _______________
4. Type of Function __________
5. x-intercepts __________________
6. Period ________
3
VI. The graph y = cot x
x
y = cot x (x,y)
0
π/6
π/4
π/3
π/2
2π/3
3π/4
5π/6
Properties of the cotangent function:
1. Domain _________________
2. Range _________________
3. Symmetry _______________
4. Type of Function __________
5. x-intercepts __________________
6. Period ________
Transformations on the Graphs of the Tangent and Cotangent Functions
y = a fnct b x + c
Ex. y = tan 3 x + 2
Ex. y = - ½ cot ¼ x - 5
4
Related documents