The graph of − ⎛ ⎞ 11. sin 1 = sin is increasing for y x ⎝ ⎟ 2 − π < < π y x = . 22. 2 2 This is in the form = −1 A = sin(ω where y A x) is decreasing for = cos y x 12. The graph of = − = 1 A ω and = 1 . Thus, the amplitude is 1 2 0 < < π x 2π 2π . and the period is = = = 4π . T 13. The largest value of = sin is 1. y x 2 14. The smallest value of = is y is −1 . in = = 6 sin(ω y A x) A the x) where = cos y x 23. 15. sin = 0 when = 0, π, 2π x x = = . ω π 6 6 = A and . Thus, the amplitude is = = = 2π 2π . d is 2 T 24. = 0 when = π , 3π . x ω π 16. 2 2 = − 3cos(3x) y the cos x = = − π 1 when 3π , ; 17. x = − 3 = cos(ω A y A x) This is in the form where sin x π 3π amplitude is =− 2 2 = −1 sin when and the period is = 2π = 2π . x T x ω = and 3 = − 3 = 3 A 2 2 . Thus, the 3 cos = 1 when = − 2π, 0, 18. x x ⎛ ⎞ 1 3 =− ⎜ ⎟ 2π; y 25. cos = −1 when = −π, x x π. ω ⎝ ⎠ 2 2 19. This is in the form = cos(ω where y A x) = 2sin y x Thus, the amplitude is This is in the form = 2 A = ω and A = sin(ω where y A x) − = 1 3 .
11. The graph of − π < x < π . y = sin x is increasing for 22. y = − sin ⎛ 1 ⎞ ⎝ 2 ⎟ 2 2 This is in the form y = A sin(ω x) where A = −1 12. The graph of y = cos x is decreasing for and ω = 1 . Thus, the amplitude is 2 A = − 1 = 1 0 < x < π . 2π 2π and the period is T = = = 4π . 13. The largest value of y = sin x is 1. 2 14. The smallest value of y = cos x is −1 . 23. y = x) is in the y = A sin(ω x) where A = 6 15. sin x = 0 when x = 0, π, 2π . and ω = π . Thus, the amplitude is A = 6 = 6 = 2π = 2π = . 16. cos x = 0 when x = π , 3π . 2 2 24. the is T 2 ω π y = − 3cos(3x) 17. sin x = 1 when x = − 3π , π ; This is in the form y = A cos(ω x) where A = − 3 sin x = −1 when x 2 2 π 3π =− 2 2 and ω = 3 . Thus, the amplitude is and the period is T = 2π = 2π . A = − 3 = 3 18. cos x = 1 when x = − 2π, 0, 2π; cos x = −1 when x = −π, π. 25. ω 3 1 ⎛ 3 ⎞ y =− ⎜ ⎟ 2 ⎝ 2 ⎠ 19. y = 2sin x This is in the form y = A cos(ω x) where This is in the form y = A sin(ω x) where A = 2 A = − 1 and ω = 3 . Thus, the amplitude is d
62514-0132318806_ISM_02-1.docx