Graphs of sin x and 2 sin x are of same shape but the maximum height of thegraph of sin x is ________ the maximum height of the graph of __________

The relationship between the graphs of $\sin x$ and $2\sin x$ can be understood by analyzing their properties.

1. Understanding the Functions:

   • The function $\sin x$ has a maximum value of 1 and a minimum value of -1.
   • The function $2\sin x$ is simply a vertical scaling of $\sin x$ by a factor of 2, meaning its maximum height will be 2 and its minimum height will be -2.

2. Comparing Maximum Heights:

   • The maximum height of the graph of $\sin x$ is 1.
   • The maximum height of the graph of $2\sin x$ is 2.

3. Final Answer: The maximum height of the graph of $\sin x$ is half the maximum height of the graph of $2\sin x$. Therefore, filling in the blanks:

   "The maximum height of the graph of $\sin x$ is half the maximum height of the graph of $2\sin x$."