A step by step tutorial on graphing and sketching arcsin functions where also the domain and range of these functions and other properties are discussed.
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Graph, Domain and Range of arcsin(x)In what follows, arcsin(x) is the inverse function of f(x) = sin(x) for - ?/2 ? x ? ?/2.The domain of y = arcsin(x) is the range of f(x) = sin(x) for -?/2 ? x ? ?/2 and is given by the interval [-1 , 1]. The range of arcsin(x) is the domain of f which is given by the interval [-?/2 , ?/2]. The graph, domain and range of both f(x) = sin(x) for -?/2 ? x ? ?/2 and arcsin(x) are shown below. ![]()
Example 1Find the domain and range of y = arcsin(x - 2) and graph it.
Solution to Example 1
The value of x is calculated from the value of x - 2. For example when x - 2 = -1, solve for x to find x = 1 and so on. The domain is given by the interval [1,3] and the range is given by the interval [-?/2,?/2] The three points will now be used to graph y = arcsin(x - 2). ![]()
Example 2Find the domain and range of y = 2 arcsin(x + 1) and graph it.
Solution to Example 2
domain = [-2,0] , range = [- ? , ?] ![]()
Example 3Find the domain and range of y = - arcsin(x - 1) and graph it.
Solution to Example 3
domain = [0 , 2] , range = [- ?/2 , ?/2] ![]() More References and Links to GraphingGraphing Functions
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