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Pg. 385 Homework

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- 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!!
- #43y = 3.61 sin (x + 0.59)
- #44y = -5.83 sin (x + 2.6)
- #46y = 5 sin (2x – 0.64)
- #51D: (∞, ∞); R: [-5.39, 5.39]; P: 2π; max (0.38, 5.39); min (3.52, -5.39)
- #9Graph
- #10Graph
- #35
- #36No Solution!!
- #37x = ±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, ∞)

Inverse Functions

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.

- What is an inverse?
- How can you tell it is an inverse both algebraically and graphically?
- Will trig functions have an inverse?

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]

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 (-∞, ∞)