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Mastering Inverse Trigonometric Functions & Identities

Learn about inverse trigonometric functions such as sine, cosine, and tangent, their domains, ranges, and applications in verifying identities. Practice evaluating inverse trig functions and understand the relationships between them. Get ready for a memorization quiz tomorrow!

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Mastering Inverse Trigonometric Functions & Identities

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  1. Pg. 395 Homework • Pg. 395 #1 – 10 allPg. 401 #19 – 23 oddPg. 407 #9Memorization quiz Tomorrow!! • #13 21.22° #15 7.13° #17 0.48 • #19 1.17 #21 π/2 #23 π/4 • #25 -π/3 #27 0.36 #29 0.42 • #31 undefined #33 undefined #35 0.74 • #37 √3/2 #39 ½ #41 0.8

  2. 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]

  3. 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 (-∞, ∞)

  4. 7.2 Inverse Trigonometric Functions Evaluating Inverse Trig sin-1 (tan(3π/4) cos(tan-1 (½)) • Keep in mind the domain of inverse trig functions when you evaluate them!! • sin-1 (0.5) • sin-1 (-0.7) • sin-1 (1.2)

  5. 7.2 Inverse Trigonometric Functions More Inverse! Verifying Identities Show thatsin-1 x +cos-1 x = π/2for all x in [-1, 1]. • Using inverse on the calculator and our brains together! • sin x = 0.6 • cot x = 2.5

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