Find the Domain y=sin(x-2)

Problem

y=sin(x−2)

Solution

1. Identify the type of function. The given equation is a sine function, which is a basic trigonometric function.

2. Determine the constraints of the input. The sine function sin(u) is defined for all real numbers u

3. Analyze the argument. The argument of the function is x−2 which is a linear polynomial. Polynomials are defined for all real numbers x

4. Conclude the domain. Since there are no values of x that result in division by zero, square roots of negative numbers, or undefined trigonometric values, the domain is all real numbers.

Final Answer

Domain: *(−∞,∞)

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