Pg. 395 Homework

• Pg. 395 #1 – 10 allPg. 401 #19 – 23 oddPg. 407 #9Memorization quiz Thursday!!

• #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• 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))

3

32

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].