Find the Domain x=-3sin(y)

Problem

x=−3*sin(y)

Solution

1. Identify the relationship between the variables. The given equation x=−3*sin(y) expresses x as a function of y To find the domain of the relation in terms of x we must determine the set of all possible values that x can take.

2. Analyze the range of the trigonometric component. The sine function, sin(y) is defined for all real numbers y and its values are always between −1 and 1 inclusive.

−1≤sin(y)≤1

3. Apply the transformations to the inequality. Multiply all parts of the inequality by −3 Note that multiplying by a negative number reverses the inequality signs.

−3*(1)≤−3*sin(y)≤−3*(−1)

−3≤−3*sin(y)≤3

4. Substitute the original variable back into the inequality. Since x=−3*sin(y) the possible values for x are restricted to the interval determined in the previous step.

−3≤x≤3

Final Answer

Domain: *[−3,3]

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