Pg. 395 Homework Pg. 395#1 – 10 all Pg. 401#19 – 23 odd Pg. 407#9 Memorization quiz Thursday!! # °#157.13°# #191.17#21π/2#23π/4 #25-π/3#270.36# #31undefined#33undefined# #37√3/2#39½ #410.8

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

7.2 Inverse Trigonometric Functions Inverse Tangent Function The inverse tangent function, denoted y = tan -1 x or y = arctan x 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 (-∞, ∞) Finding the Domain and Range. Graph. f(x) = 2sin -1 (4x) g(x) = cos -1 (¾ x) – π

7.2 Inverse Trigonometric Functions Evaluating Inverse Trig 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) Solve without a calculator. tan -1 ( ) cos -1 ( ) sin -1 (-1) sin -1 (tan(3π/4) cos(tan -1 (0)) tan(arctan(3))

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