# Chapter 4 - Graphs of the Circular Functions - Section 4.1 Graphs of the Sine and Cosine Functions - 4.1 Exercises - Page 152: 61

In general, $\sin{(bx)} \ne b\cdot \sin{x}$.. This is because they have different periods and amplitudes. Refer to the image in the step by step part below for the graph.

#### Work Step by Step

RECALL: The function $a \cdot \sin{(bx)}$ has : amplitude = $|a|$ period = $\frac{2\pi}{b}$ Thus: The function $y=\sin{(2x)}$ has an amplitude of $|1|=1$ and a period of $\frac{2\pi}{2} = \pi$. The function $y=2\sin{x}$ has an amplitude of $|2|=2$ and a period of $\frac{2\pi}{1}=2\pi$. From the information above, it is bvious that the t wo functions are different from each other. Thus, it cannot be said that in general, $\sin{(bx)}=b \cdot \sin{x}$. Use a graphing utility to graph the two functions. (Refer to the attached image below for the graph, the green graph is $y=2\sin{x}$ while the red graph is $y=2\sin{x}$.) Use a graphing utility to graph the given functions. (Refer to the graph below.) Notice that the graphs are different.

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