1. Graphing Trigonometric Functions Objective: To graph various trigonometric functions. VERTICAL DISPLACEMENT The graph of y = A sin(k  + c) + h is the graph of y = A sin(k  + c) translated h units vertically. If h > 0, the graph is moved up, and if h < 0 then the graph is moved down. This applies to all the trig functions.

2. G RAPH Y = COS  AND Y = COS  -1 ON THE SAME SET OF AXES. E XPLAIN THE SIMILARITIES AND DIFFERENCES BETWEEN THE GRAPHS.  0°45°90°135°180°225°270°315°360° Cos  10.710-0.71-0.7100.711 Cos  - 1 0-0.29-1.71-2-1.71-0.290

3. G RAPH Y = 4 SIN 2  Find the amplitude, period and phase shift. Amplitude = |A| = 4Period = 360 2 = 180° Phase Shift = 0202 = 0

4. G RAPH Y = TAN ( ) x - p 2 6 Period = ½½ = 2  Phase Shift = -  6. ½ = 33

5. Compound functions may consist of sums or products of trigonometric functions. For example, y = sin x ∙ cos x is a compound function that contains a product of trig functions. Compound functions can also include sums or products of trig functions and other functions. For example, y = sin x + x is a compound function that is the sum of a trig function and a linear function. Compound Functions

6. Graph y = sin x + x x 0  2  3  /222 5  /233 sin x 010010 sin x + x 02.573.143.716.288.859+.42 ● ● ● ● ● ● ●

7. Graph y = x cos x x 0  /2  3  /222 5  /233 y = x 0  /2  3  /222 5  /233 y = cos x 10010 y = x cos x 00 -- 0 22 0 -3 

8. A SSIGNMENT Page 326 # 13 - 30