Multiple Choice
For the topic of graphs of the sine and cosine functions, what is the axis of symmetry for the graph of ?
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4. Graphing Trigonometric Functions
Graphs of the Sine and Cosine Functions
Multiple Choice
What is the maximum value of over all real numbers ?
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Verified step by step guidance1
Recall the definition of the sine function: \(f(x) = \sin(x)\), which is a periodic function with values oscillating between -1 and 1 for all real numbers \(x\).
Understand that the sine function reaches its maximum value at specific points where the angle \(x\) corresponds to \(\frac{\pi}{2} + 2k\pi\), where \(k\) is any integer.
Recognize that the maximum value of \(\sin(x)\) is 1, which occurs at these points because the sine of \(\frac{\pi}{2}\) is 1.
Therefore, the maximum value of \(f(x) = \sin(x)\) over all real numbers \(x\) is 1.
No matter what real number \(x\) you choose, \(\sin(x)\) will never exceed 1, confirming that 1 is the absolute maximum.
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