Find the Domain y=3cos(x)

Problem

y=3*cos(x)

Solution

1. Identify the type of function. The given equation y=3*cos(x) is a transformation of the basic trigonometric function ƒ(x)=cos(x)

2. Recall the domain of the parent function. The cosine function cos(x) is defined for all real numbers because the angle x can take any value on the unit circle.

3. Analyze the transformations. The coefficient 3 represents a vertical stretch, which affects the range of the function but does not impose any restrictions on the input x

4. Determine the domain. Since there are no denominators, square roots of negative numbers, or logarithms, there are no restrictions on x

Final Answer

Domain: *(−∞,∞)

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