|
|
|
The exploration is carried out by analyzing the effects of the parameters a, b, c and d included in the definition of arcsin as follows
f(x) = a*Arcsin(b*x + c) + d
Interactive Tutorial
click on the button above "click here to start" and MAXIMIZE the window obtained.
- Set the parameters to a = 1, b = 1, c = 0 and d = 0 to obtain
f(x) = arcsin(x)
Check that the domain of arcsin(x) is given by the interval [-1 , 1] and the range is given by the interval [-pi/2 , +pi/2](pi/2 is approximately 1.57).
- Change parameter a and note how the graph of arcsin changes (vertical compression, stretching, reflection). How does it affect the range of the arcsin function?
Does a change in parameter a changes the domain of arcsin?
- Change parameter b and note how the graph of arcsin changes (horizontal compression, stretching). Does a change in b affect the domain of arcsin? range?
- Change parameter c and note how the graph of arcsin changes (horizontal shift). Does a change in c affect the domain of arcsin? range?
- Change parameter d and note how the graph of arcsin changes (vertical shift). Does a change in d affect the range of arcsin? domain?
- If the range of arcsin(x) is given by the interval [-pi/2 , +pi/2] what is the range of a*arcsin(x)? What is the range of a*arcsin(x)+ d?
- What is the domain and range of a*arcsin(bx + c)+ d?
Exercises
- Find the domain and range of f(x) = arcsin(x - 1) - 2 and graph f.
- Find the domain and range of g(x) = -arcsin(x + 1) + 2 and graph g.
- Find the domain and range of h(x) = -2arcsin(x + 1) -1 and graph h.
More on Inverse Trigonometric Functions
|
|