
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
Change parameters a, b, c and d and click on the button 'draw' in the left panel below.
 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 [π/2 , +π/2](π/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 [π/2 , π/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 References and Links to Inverse Trigonometric Functions
Inverse Trigonometric Functions
Graph, Domain and Range of Arcsin function
Graph, Domain and Range of Arctan function
Find Domain and Range of Arccosine Functions
Find Domain and Range of Arcsine Functions
Solve Inverse Trigonometric Functions Questions
