Find the Domain and Range f(x)=sin(x)

Problem

ƒ(x)=sin(x)

Solution

1. Identify the domain of the sine function. The function sin(x) is defined for all real numbers because there are no values of x that result in division by zero or an undefined operation.

D=(−∞,∞)

2. Determine the range by considering the behavior of the unit circle or the graph of the function. The sine function oscillates between a minimum value of −1 and a maximum value of 1

−1≤sin(x)≤1

3. State the range in interval notation based on these bounds.

R=[−1,1]

Final Answer

Domain: *(−∞,∞), Range: *[−1,1]

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