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Pg. 385 Homework

Pg. 385 Homework. Pg. 395 #13 – 41 odd, graph the three inverse trig functions and label the domain and range of each. Memorization quiz through inverse trig functions on Thursday!! #43 y = 3.61 sin ( x + 0.59) #44 y = -5.83 sin ( x + 2.6)

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Pg. 385 Homework

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  1. Pg. 385 Homework • Pg. 395 #13 – 41 odd, graph the three inverse trig functions and label the domain and range of each.Memorization quiz through inverse trig functions on Thursday!! • #43 y = 3.61 sin (x + 0.59) • #44 y = -5.83 sin (x + 2.6) • #46 y = 5 sin (2x – 0.64) • #51 D: (∞, ∞); R: [-5.39, 5.39]; P: 2π; max (0.38, 5.39); min (3.52, -5.39) • #9 Graph • #10 Graph • #35 • #36 No Solution!! • #37 x = ±2.66 + 4kπ, where k is any integer • #38 (-3.98, -3.75)U(-1.39, 0)U(1.39, 3.75)U(3.98, ∞)

  2. 7.2 Inverse Trigonometric Functions Inverse Functions Inverse sin x Consider y = sin x on the interval [-π/2, π/2]. Will it pass the HLT? Will it have an inverse? An inverse can be defined as long as the domain of the original function lends itself to an inverse. • What is an inverse? • How can you tell it is an inverse both algebraically and graphically? • Will trig functions have an inverse?

  3. 7.2 Inverse Trigonometric Functions Inverse Sine Function Inverse Cosine Functions The inverse cosine function, denoted y = cos-1 x or y = arccosx is the function with a domain of [-1, 1] and a range of [0, π] that satisfies the relation cosy = x. If f(x) = cosx and f-1(x) = cos-1 x(f-1 ◦ f)(x) = x on [0, π] and(f ◦ f-1)(x) = x on [-1, 1] • The inverse sine function, denoted y = sin-1 x or y = arcsinx is the function with a domain of [-1, 1] and a range of [-π/2, π/2] that satisfies the relation sin y = x. • If f(x) = sin x and f-1(x) = sin-1 x(f-1 ◦ f)(x) = x on [-π/2, π/2] and(f ◦ f-1)(x) = x on [-1, 1]

  4. 7.2 Inverse Trigonometric Functions Inverse Tangent Function Finding the Domain and Range f(x) = sin-1 (2x) g(x) = sin-1 (⅓ x) • The inverse tangent function, denoted y = tan-1 x or y = arctanx is the function with a domain of (-∞, ∞) and a range of (-π/2, π/2) that satisfies the relation tan y = x. • If f(x) = tan x and f-1(x) = tan-1 x(f-1 ◦ f)(x) = x on (-π/2, π/2) and(f ◦ f-1)(x) = x on (-∞, ∞)

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