Chapter 13.4, Problem 8E

Solution

To find: The graph of the given functions and obtain the similarities and differences.

Amplitude and period are the same. The difference is that the curves go in the opposite direction after starting from the origin.

Given:

The functions $y=\sin x$ and $y=\cos \left(x+\frac{\pi }{2}\right)$ .

Concept used:

Substitute the given function in the graphing calculator to obtain the graph of the function.

Calculation:

The graph of $y=\sin x$ and $y=\cos \left(x+\frac{\pi }{2}\right)$ have been drawn below using the graphing calculator. The blue curve represents the $y=\sin x$ and the black curve represents $y=\cos \left(x+\frac{\pi }{2}\right)$ .

  

From the above graph, it is understood that the amplitude and period of both functions are the same. The difference is that the curve of $y=\sin x$ and $y=\cos \left(x+\frac{\pi }{2}\right)$ goes in the opposite direction after starting from the origin.

Conclusion:

Hence, the amplitude and period are the same whereas the direction after starting from the origin is different.