Math III Accelerated

1. Math III Accelerated Chapter 14 Trigonometric Graphs, Identities, and Equations

2. Warm Up 14.2 • Describe the translation of the graph of y = x2 that produces the graph of the given function.

3. 14.2Translate and Reflect Trigonometric Graphs • Objective: • Translate and graph trigonometric graphs.

4. Translations of Sine & Cosine • To graph y = a sin b(x – h) + k or y = acosb(x – h) + k(a > 0 and b > 0): • Identify: Amplitude, a Period, 2π/b Horizontal shift, h Vertical shift, k • Draw: Horizontal line y = k. (MIDLINE) • Find the 5 key points: Translate the 5 key points of y = a sin bxor y = acosbx • Draw the graph.

5. Example 1 • Graph y = 3 sin 2x + 1. Amplitude _______ Horiz. Shift _______ Period _______ Vert. Shift _______ Midline _______ Key Points

6. Checkpoint 1 • Graph y = 4 sin 2x + 3. Amplitude _______ Horiz. Shift _______ Period _______ Vert. Shift _______ Midline _______ Key Points

7. Example 2 • Graph . Amplitude _______ Horiz. Shift _______ Period _______ Vert. Shift _______ Midline _______ Key Points

8. Checkpoint 2 • Graph y = –2 cos (x + π). Amplitude _______ Horiz. Shift _______ Period _______ Vert. Shift _______ Midline _______ Key Points

9. Example 3 • You watch a classmate lower a flag on a 20-foot flagpole. You are standing 15 feet from the base of the flagpole. Write and graph a model that gives the flag’s distance d (in feet) from the top of the flagpole as a function of the angle of elevation θ.

10. Example 3 d 30 Distance (feet) 20 20 - d 10 θ 0 40 0 20 60 15 ft Angle (degrees)

11. Checkpoint 3 • Write and graph a model for Example 3 if you stand 10 feet from the flagpole.

12. Homework 14.2 • Practice 14.2

13. HW Review • Graph y Amplitude _______ Horiz. Shift _______ Period _______ Vert. Shift _______ Midline _______ Key Points