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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!!. 7.2 Inverse Trigonometric Functions. Inverse Functions. Inverse sin x.

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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!!

  2. 7.2 Inverse Trigonometric Functions Inverse Functions Inverse sin x Consider y = sin x. Will it pass the HLT? Will it have an inverse? An inverse function can be defined as long as the domain of the original function lends itself to an inverse function. Consider y = sin x on the interval [-π/2, π/2]. Will it pass the HLT? Will it have an inverse function? • What is an inverse? • How can you tell it is an inverse both algebraically and graphically? • Will f(x) = x – 4 have an inverse? • If so, prove it algebraically and graphically.

  3. 7.2 Inverse Trigonometric Functions Inverse Sine Function Inverse cosx Consider y = cosx. Will it pass the HLT? Will it have an inverse function? Consider y = cosx on the interval [0, π]. Will it pass the HLT? Will it have an inverse function? • 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 Cosine Function Inverse Tangent Function 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 (-∞, ∞) • 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]

  5. 7.2 Inverse Trigonometric Functions Find the Domain and Range.Graph. h(x) = cos-1 (3x) k(x) = cos-1 (⅕ x) • f(x) = sin-1 (2x) • g(x) = sin-1 (⅓ x)

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