The Graphs of other Trig Functions
What is the tan(0)?_______________________
What should be observed in the graph of tangent at the x-value of
0?_______________________
Where else will these occur from [−2π , 2π ] ?____________________________
[
]
Sketch the graph of tangent of x. on the interval − 3 π , 3 π
2 2
4
3
2
1
-6.28319 -3.14159
3.14159
6.28319
-1
-2
-3
-4
What is the amplitude of tan(x)? _______________________________________
What is the period of tan(x)? __________________________________________
What is the midpoint between any two consecutive asymptotes?______________
Complete the following Table
xvalue
−π
2
-1.5707
-1.57
-1.4
-1.1
0
1.1
1.4
1.57
1.5707
Tan(x)
−π
π
and .
2
2
________________________________________________________________________
Describe the behavior of the tangent curve as x approaches
________________________________________________________________________
Based on what we know of period, what will be the period of the function y = tan (2 x ) ?
______________________________
Verify Graphically.
4
3
2
1
-6.28319 -4.71239 -3.14159 -1.5708
1.5708
3.14159 4.71239 6.28319
-1
-2
-3
-4
If we graph y = 3 ⋅ tan (2 x ) , what will be the difference if any?
________________________________________________________________________
What if we graph y = −3 ⋅ tan (2 x ) , conjecture about the graph.
________________________________________________________________________
π
2
Plot both along with the tan (x) .
2
1
-3.14159 -2.35619 -1.5708 -0.785398
0.785398 1.5708 2.35619 3.14159
-1
-2
Were your thoughts correct?_________________________________________________
The interval for tangent is usually written
−π
π
< x < . Without graphing where will
2
2
the vertical asymptotes of y = tan (.5x) hint: solve the inequality with (.5x) taking the
role of x. ____________________________________________________________
What is the period?___________________________________________________
Sketch the graphs of y = cos(x) and y = sec(x) on the same axes.
4
3
2
1
-6.28319
-3.14159
3.14159
-1
-2
-3
-4
6.28319
Complete the following table (Don’t forget that the sec(x) = 1/cos(x) )
x-value 0
.5
.75
.9
1
1.3
1.4
1.5
1.57
π
2
cos(x)
sec(x)
Describe the behavior for both functions as x approaches
π
2
________________________________________________________________________
________________________________________________________________________
Explain how the table correlates to what you see graphically above: Be very Specific
________________________________________________________________________
Where else will similar behavior occur for the secant function?
________________________________________________________________________
________________________________________________________________________
What is the period for y = sec(x)? ____________________________
Sketch the graphs of y = sin(x) and y = csc(x) on the same axes.
4
3
2
1
-6.28319 -4.71239 -3.14159 -1.5708
1.5708
-1
-2
-3
-4
3.14159 4.71239 6.28319
Complete the following table (Don’t forget that the csc(x) = 1/sin(x) )
x-value 0
.5
.75
.9
1
1.3
1.4
1.5
1.57
π
2
sin(x)
csc(x)
Describe the behavior for both functions as x approaches
π
2
________________________________________________________________________
________________________________________________________________________
Explain how the table correlates to what you see graphically above: Be very Specific
________________________________________________________________________
________________________________________________________________________
Where else will similar behavior occur for the cosecant function?
________________________________________________________________________
________________________________________________________________________
Graph y = csc(x +
π
4
)
4
3
2
1
-6.28319 -4.71239 -3.14159
-1.5708
1.5708
3.14159
4.71239
-1
-2
-3
-4
What do you suspect that the period of y = csc(2x) is? Verify graphically.
4
3
2
1
-6.28319 -4.71239 -3.14159
-1.5708
1.5708
-1
-2
-3
-4
Does this relate to what we did before? Explain.
3.14159
4.71239
6.28319
6.28319