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 5 2,18 3 18 3

x k x k

7.2 Inverse Trigonometric Functions

Inverse Functions• What is an inverse?• How can you tell it is an

inverse both algebraically and graphically?

• Will trig functions have an inverse?

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.

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

• f(x) = sin-1 (2x)

• g(x) = sin-1 (⅓ x)