Advanced Algebra 2 Name Graphing Trig Functions 1. Shift (horizontal .

Advanced Algebra 2 Name Name: Functions Graphing Trig Worksheet 3 Graphing Sine and Cosine - worksheet 8.1/8.2 Advanced Algebra Advanced Algebra 22 ALT12 ALT12 ALT12 Name Name FST Worksheet Worksheet 33 1. each the trigonometric functions, state amplitude, period, vertical shift, and and phase Forof of the following trigonometric functions, state the amplitude, vertical shift,phase and phase 1. For For1. each ofeach the following following trigonometric functions, state the the amplitude, period,period, vertical shift, shift (horizontal shift). Then graph the function, completely filling in the independent axis. shift (horizontal Then graph the function, completely the independent shift (horizontal shift). shift). Then graph the function, completely filling filling in the in independent axis. axis. (Exercises) (a) y 2 sin (a) (a)2 sin y 2 sin 1. y 4 4 y y y 4 2 2 2 360 180 360 180 180 360 360 180 180 360 180 2 360 2 2 4 4 (b) y 12 cos (b) y 12 cos 4 Amplitude: the vertical distance from the top4toyythe middle (b) y 12 cos 4 Period: the horizontal distance from beginning to endy of one wave 2 4 2 Phase Shift: a horizontal shift: 360 180 360 2 180 Vertical Shift: a vertical shift: 2 180 360 180 360 2 360 180 180 4 360 4 (c) 2. y sin(3 ) (c) y sin(3 ) 2 y 4 y 4 4 2 (c) y sin(3 ) 360 2 y 180 180 360 180 360 4 360 180 2 2 2 4 4 360 180 180 Amplitude: the vertical distance from the top to the middle Advanced Algebra 2: ALT 12 Worksheet 3 – Page 1 of 4 2 Period: the horizontal distance from beginning to end3of– Page one wave Advanced Algebra 2: ALT 12 Worksheet 1 of 4 Answers: Phase Shift: a horizontal shift: 4 Answers: Vertical Shift: a vertical shift: Advanced Algebra 2: ALT 12 Worksheet 3 – Page 1 of 4 Answers: 360

1. For each of the following trigonometric functions, state the amplitude, period, vertical shift, and phase shift (horizontal shift). Then graph the function, completely filling in the independent axis. (a) y 2 sin 3. y cosθ 2 y 4 2 (d) y cos( 90 ) 1 360 y 180 180 360 4 2 2 4 1 (b) y 360 cos 2 180 Amplitude: 180 Period: y 4 360 Vertical Shift: 2 2 4 (e)4.y y 3 5* ,(2.) 5 sin(2 ) 3 360 180 180 360 y 2 10 4 5 (c) y sin(3 ) 360 y 180 180 360 4 5 2 Advanced Algebra 2 360 ALT12 (f) y Name 10 180 180 2 cos 3 ( 90 ) 2 Amplitude: y 2 Period: 360 Vertical Shift: Worksheet 34 4 1. For each of the following trigonometric functions, state 2the amplitude, period, vertical shift, and phase shift (horizontal shift). Then graph the function, completely filling in the independent axis. (a) y 360 2 sin 180 6. 2 234*.Advanced 2 Algebra 2: ALT 12 Worksheet 3 – Page 1 of 4 180 360 y 4 2 Answers: 2 4 2. Write an equation of a sine function with amplitude of 3 and a period of 360 . 360 180 180 360 2 3. Write an equation of a cosine function with amplitude of 5 and a phase shift of 70 to the right. 4 4. Write an equation of a sine function with a vertical shift of up 3 and period of 90 . 1 (b) y an equation cos of a cosine function with a vertical shift of up 3 and phase shift of 90 to the left. 2 5. Write Amplitude: Period: Vertical Shift: y 4 2 360 180 180 Advanced Algebra 2: ALT 12 Worksheet 3 – Page 2 of 4 2 Answers: 4 360

7. Write an equation of a sine function with amplitude of 3 and period of 360 . 8. Write an equation of a cosine function with a vertical shift up 3 and period of 360 . 9. Write an equation of a sine function with amplitude of 8, a vertical shift down 4, and a period of 2 . Advanced Algebra 2 Name ALT12 10. Write an equation of a cosine function with amplitude of -2, a vertical shift up 3, and a Worksheet 4 period of . 1. For each of the following trigonometric functions, state the amplitude, period, vertical shift, and phase shift (horizontal shift). Then graph the function, completely filling in the independent axis. (a) y 2 cos x8 11. % )* , 1 9 y 4 (d) y cos 2 x 2 2 1 x 2 y 2 2 4 2 2 4 x (b) y sin x Amplitude: 2 1 2 Period: 2 Vertical Shift: y 44 2 (e)12. y 5% 55sin(2x) sin(2,) 5 x 2 2 10 2 2 y 4 5 (c) y 2 cos(4x) x 1 5 y 4 10 2 (f)Amplitude: y 2 2 cos 4 (x 2 ) 2 Period: 2 y 4 4 2 x Vertical Shift: 2

FST Name: Period: Date: Graphing Sine and Cosine: Assignment 8.3 Advanced Algebra 2 ALT12 Name For each of the following trigonometric functions, Worksheet 3 state the amplitude, length of period, vertical shift, and phase shift. Then graph the function, filling in the independent axis. 1. For each of the following trigonometric functions, state the amplitude, period, vertical shift, and phase shift (horizontal shift). Then graph the function, completely filling in the independent axis. 1. ! # %(' 90) (a) y 2 sin y 4 2 360 180 180 360 2 4 (b) Algebra y 12 cos Advanced 2 Amplitude: ALT12 Name y Period: 4 Phase Shift: Worksheet 3 Vertical Shift: 2 1. For each of the following trigonometric functions, state the amplitude, period, vertical shift, and phase 360 180 180 360 shift (horizontal shift). Then graph the function, completely filling in the independent axis. 2. ! ,-#(' 180) 1 (a) y 2 sin 2 y 4 4 (c) y sin(3 ) 2 y 4 360 180 180 360 180 360 2 2 360 (b) y 1 2 4 180 cos 2 y Amplitude: 4 4 Period: Phase Shift: 2 Vertical Shift: Advanced Algebra 2: ALT 12 Worksheet 3 – Page 1 of 4 360 180 180 Answers: 2 4 (c) y sin(3 ) 360

1. For each of the following trigonometric functions, state the amplitude, period, vertical shift, and phase shift (horizontal shift). Then graph the function, completely filling in the independent axis. 13.y 2!cos x 2 &'((2*) 1 (a) y 4 2 x 2 Advanced Algebra 2 ALT12 2 Name 2 4 Worksheet 4 (b) y 12 sin x Amplitude: Period: Vertical Shift: 1. For each of the following trigonometric functions, state they amplitude, period, vertical shift, and phase 4 shift (horizontal shift). Then graph the function, completely filling in the independent axis. 14.y 2!cos x (./* 3 (a) 2 x 2 2 y 42 24 (c) y 2 cos(4x) 1 x 2 2 y 4 4 (b) y 12 sin x Amplitude: 2 2 Period: x Vertical Shift: 42 2 y 24 x 2 15. 2 Write an equation of a cosine function with amplitude 0.6, period of 1, and a vertical shift up 3. 2 4 (c) y Advanced Algebra 2: ALT 12 Worksheet 4 – Page 1 of 2 cos(4x) 1 Answers: 16. Write an equation of a sine function with amplitude 3, a vertical shift down 6, and a y 1 period of 2. 4 2 x 2 2 4 2

1. For each of the following trigonometric functions, state the amplitude, period, vertical shift, and phase shift (horizontal shift). Then graph the function, completely filling in the independent axis. (3(θ 90)) 2sin 3.(a) y y 2 sin y 4 2 360 180 180 Advanced Algebra 2 ALT12 360 Name 2 4 Worksheet 4 (b) y 12 cos Amplitude: Period: 1. For each of the following trigonometric functions, state4they amplitude, period, vertical shift, and phase shift (horizontal shift). Then graph the function, completely filling in the independent axis. Phase Shift: Vertical Shift: 2 (a) y 2 cos x 1 4. y cos (θ π ) 2 360 180 180 y 360 4 2 2 x 4 2 Advanced Algebra 2 (c) y sin(3 ) ALT12 Name 2 2 y 4 4 Worksheet 4 2 (b) y 12 sin x Amplitude: Period: 1. For each of the following trigonometric functions, state the amplitude, period, vertical shift, and phase shift (horizontal shift). Then graph the function, completely filling inShift: the independent axis. y 360 180 180 360 Phase Shift: Vertical 4 (a) y 2 cos x y cos ( 2θ π ) 2 2 5. 2 4 2 x y 4 2 2 2 4 Advanced Algebra 2: ALT 12 Worksheet 3 – Page 1 of 4 (c) y 2 cos(4x) 1 Answers: 2 4 4 1 (b) y sin x Amplitude: 2 x 2 2 Phase Shift: 2 y Period: y Vertical Shift: x 2 4 2 2 4 x 2 2

1. For each of the following trigonometric functions, state the amplitude, period, vertical shift, and phase shift (horizontal shift). Then graph the function, completely filling in the independent axis. 2sin 6.(a) y y 2 sin ( 2θ 180 ) 2 y 4 2 Advanced Algebra 2 360 ALT12 Name180 180 360 2 Worksheet 4 4 1 the following 1. For of trigonometric functions, state thePeriod: amplitude, period, vertical shift, and phase (b) each y Amplitude: cos 2 shift (horizontal shift). Then graph the function, completely filling in the independent axis. y 4 Phase Shift: Vertical Shift: (a) y 2 cos x 7. 2 y 2 cos (θ π ) 2 y 4 360 180 180 360 2 2 x 2 4 2 2 (c) y sin(3 ) 4 y 4 1 (b) y sin x Amplitude: 2 Phase Shift: 360 8. 180 Period: 2 4 y Vertical Shift: 180 360 22 Write an equation of a sine function with amplitude of 3, a vertical shift up 2 and a period x of2 360 . 4 2 2 4 AdvancedofAlgebra 2: ALT 12 Worksheet 3 – Page 1 of Write an equation a cosine function with amplitude of45 and a phase shift of 70 to the right. (c) y cos(4x) 1 9. Answers: y 4 10. 1 Write an equation of a sine function with a vertical shift of 3 and period of 2 . 2 x 2 11. Write an equation of a cosine function2with a vertical shift of 3, a period of 180 , 5n amplitude of 3, and a phase shift of 90 to the left. 4 2

For each of the following trigonometric functions, state the amplitude, period, vertical shift, and phase shift (horizontal shift). Then graph the function, completely filling in the independent axis. (a) y 2sin y 360 180 180 360 4 2 2 4 (b) y 1 2 cos y 360 180 180 360 4 2 2 4 (c) y sin(3 ) y 360 180 180 360 4 2 2 4