Solving Trig Equations Graphically



Solving Trig Equations Graphically Name_________________________

Functional Analysis: Section 4.4 Date__________ Period_________

Consider the graph of ((x).

[pic]

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, 2(] by [-1, 1]. Sketch it here.

0 ( 2(

-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, 2(] by [-1, 1]. Sketch it here.

0 ( 2(

-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. [pic] 2. [pic]

3. [pic] 4. [pic]

5. [pic] 6. [pic]

7. [pic]

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