Solving Trig Equations Graphically Name______
Functional Analysis: Section 4.4 Date______Period______
Consider the graph of ¦(x).
1. Amplitude ______2. Period ______3. Midline ______
4. Find two different values of c (the phase shift) that could be ______
used if you were writing an equation using cosine.
5. The phase shift for cosine can be found by choosing the x-coordinate of any ______.
6. In your calculator, graph y = cos x using the following window 1
[0, 2p] by [-1, 1]. Sketch it here.
0 p 2p
-1
7. Now graph y = -cos x using the same window. Using a different color, sketch it over top of your graph in #6. How did the graph change?
8. The phase shift for negative cosine can be found by choosing the x-coordinate of any ______.
9. Going back to ¦(x) above, find two different values of c (the phase shift ______
that could be used if you were writing an equation using negative cosine.
10. Find two different values of c (the phase shift) that could be ______
used if you were writing an equation using sine.
11. The phase shift for sine can be found by choosing the x-coordinate of any ______where the function is ______.
12. In your calculator, graph y = sin x using the following window 1
[0, 2p] by [-1, 1]. Sketch it here.
0 p 2p
-1
13. Now graph y = - sin x using the same window. Using a different color, sketch it over top of your graph in #12. How did the graph change?
14. The phase shift for negative sine can be found by choosing the x-coordinate of any ______where the function is ______.
15. Going back to ¦(x) above, find two different values of c (the phase shift ______
that could be used if you were writing an equation using negative sine.
Practice Find an equation for each of the following graphs. You must use one of the trig functions (sin, cos, - sin, - cos) at least once. Try to write the equations so that the phase shift is zero (C = 0).
1. 2.
3. 4.
5. 6.
Now, let’s sketch the following without using our calculator.
1. 2.
3. 4.
5. 6.
7.