Consider the function $f\left(x\right)=\cos\left(x+\frac{\pi}{2}\right)$.

1. Make a complete graph of $f(x)$.

   Answer (a):

   

2. Write a simpler trig function that is represented by the same graph.

   Hint (b):

   Which trig function passes through the origin?

3. Now use the angle sum identity to expand and simplify $\cos\left(x+\frac{\pi}{2}\right)$.

   Hint (c):

   Use Angle Sum Identities.

4. Does your work in part (c) agree with your graphical results from parts (a) and (b)? Explain.

   Hint (d):

   Your answers should agree.