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

1. Make a complete graph of the function.

   Answer (a):

   

2. Write a simpler trigonometric 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 $\cos(x+\frac{\pi}{2})$.

   Hint (c):

   Review the Math Notes box in this lesson and problem 12-108 for the 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.