4.3 Sine Function and Inverse Sine Function

. Sine Function and Inverse Sine Function Let us recall that sine function is a function with  as its domain and [ , ] - as its range. We write y = sin and y sin or y = arcsin( ) to represent the sine function and the inverse sine function, respectively. Here, the symbol - is not an exponent.

It denotes the inverse and does not mean the reciprocal. We know that sin ) = π is true for all real numbers x . Also, sin x ) need not be equal to sin x for < < π and for all x . Hence, the period of the sine function is p .

. . The graph of sine function The graph of the sine function is the graph of y = sin , where x is a real number. Since sine function is periodic with period p , the graph of the sine function is repeating the same pattern in each of the intervals,  , − ] ,  .

Therefore, it suffices to determine the portion of the graph for x ∈ [ ] , π . Let us construct the following table to identify some known coordinate pairs for the points ( , ) x y on the graph of y = sin