### Home > A2C > Chapter 13 > Lesson 13.2.3 > Problem13-132

13-132.
1. Consider the function. Homework Help ✎

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

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

3. Now use the angle sum identity to expand and simplify .

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

$\text{This function is just the graph of } y=\text{cos}(x) \text{ shifted }\frac{\pi}{2} \text{ units to the left.}$

$\text{Remember the rule that sin}(x)=\text{cos}\left(\frac{\pi}{2}-x\right)$

f(x) = −sin(x)

$\text{cos}\left(x+\frac{\pi}{2}\right)=\text{cos}(x)\text{cos}\left(\frac{\pi}{2}\right)-\text{sin}(x)\text{sin}\left(\frac{\pi}{2}\right)$

Yes, they do agree.