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Can you please help me with the sine parent function(I just need the basic function for it)

Can you please help me with the sine parent function(I just need the basic function-example-1
Can you please help me with the sine parent function(I just need the basic function-example-1
Can you please help me with the sine parent function(I just need the basic function-example-2
User Mck
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1 Answer

13 votes
13 votes

We need to find some points, graph, and identify the domain and range for the sine function:


y=\sin x

To find some of the points on the graph, we can choose some values of x and then find the respective values of y:


\begin{gathered} \frac{x\ldots\ldots\ldots\ldots\ldots\ldots\ldots y}{} \\ 0\ldots\ldots\ldots\ldots\ldots\ldots\ldots0 \\ (\pi)/(2)\ldots\ldots\ldots\ldots\ldots\ldots\ldots1 \\ \pi\ldots\ldots\ldots\ldots\ldots\ldots\ldots0 \\ (3\pi)/(2)\ldots\ldots\ldots\ldots\ldots\ldots-1 \\ 2\pi\ldots\ldots\ldots\ldots\ldots\ldots\ldots0 \\ -(\pi)/(2)\ldots\ldots\ldots\ldots\ldots\ldots-1 \\ -\pi\ldots\ldots\ldots\ldots\ldots\ldots\ldots0 \\ -(3\pi)/(2)\ldots\ldots\ldots\ldots\ldots\ldots1 \\ -2\pi\ldots\ldots\ldots\ldots\ldots\ldots\ldots0 \end{gathered}

Now, we can plot those points and join them smoothly to obtain the graph:

The graph continues indefinity for infinitely negative and positive values of x. Thus, the domain of this function is:


\begin{gathered} \text{domain: }(-\infty,\infty) \\ or \\ \mleft\lbrace x\in\mathfrak{\Re }\mright\rbrace \end{gathered}

And since y can only have values between -1 and 1 (including -1 and 1), we have:


\begin{gathered} \text{range: }\lbrack-1,1\rbrack \\ or \\ \mleft\lbrace \mright?y\in\mathfrak{\Re }|-1\le y\le1\} \end{gathered}

Can you please help me with the sine parent function(I just need the basic function-example-1
User Minnette
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2.7k points