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 Monday!!

7.2 Inverse Trigonometric Functions

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

inverse both algebraically and graphically?

• Will f(x) = x2 – 4 have an inverse?– If so, prove it algebraically

and graphically.

Inverse sin x• Consider y = sin x. Will it pass

the HLT? Will it have an inverse?

• An inverse function can be defined as long as the domain of the original function lends itself to an inverse function.

• Consider y = sin x on the interval [-π/2, π/2]. Will it pass the HLT? Will it have an inverse function?

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 cos x• Consider y = cos x. Will it

pass the HLT? Will it have an inverse function?

• Consider y = cos x on the interval [0, π]. Will it pass the HLT? Will it have an inverse function?

7.2 Inverse Trigonometric Functions

Inverse Cosine Function• 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]

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 (-∞, ∞)

7.2 Inverse Trigonometric Functions

Find the Domain and Range.Graph.

• f(x) = sin-1 (2x)

• g(x) = sin-1 (⅓ x)

• h(x) = cos-1 (3x)

• k(x) = cos-1 (⅕ x)