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Pg. 395 Homework. Pg. 395 # 1 – 10 all Pg. 401 #19 – 23 odd Pg. 407 #9 Memorization 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.
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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
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]
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 (-∞, ∞)
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)
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