# Question Video: Finding the Domain of a Given Sine Function Mathematics

Find the domain of the function π(π) = 5 sin (π) + 4.

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### Video Transcript

Find the domain of the function π of π equals five sin π plus four.

We recall first that, in general, the domain of a function π of π is the set of all possible input values π such that the function is defined. The function weβre interested in here is π of π is equal to five sin π plus four. We recall that the domain of the sine function itself is the set of all real numbers, which we can write as the open interval from negative β to β.

In order to answer this question, we need to consider the functional transformations that have been applied to sin π to give five sin π plus four. Multiplying sin π by five is a vertical stretch of the function by a scale factor of five. Adding four to the function is a vertical shift four units up, or we may say by four units in the positive π¦-direction. Each of these transformations has a vertical effect. And so they each affect the output values or range of the sine function. Thereβs been no change to the input of the function, and so the domain is unaffected.

The domain of the function π of π is, therefore, the same as the domain of the sine function, which is the open interval from negative β to positive β.