Pg. 395 Homework
• Pg. 395 #1 – 10 all
Pg. 401 #19 – 23 odd
Pg. 407 #9
Memorization quiz Thursday!!
•
•
•
•
•
#13
#19
#25
#31
#37
21.22°
1.17
-π/3
undefined
√3/2
#15
#21
#27
#33
#39
7.13°
π/2
0.36
undefined
½
#17
#23
#29
#35
#41
0.48
π/4
0.42
0.74
0.8
7.2 Inverse Trigonometric Functions
Inverse Sine Function
Inverse Cosine Functions
• The inverse sine function,
• The inverse cosine function,
denoted y = sin-1 x or
denoted y = cos-1 x or
y = arcsin x is the function
y = arccos x is the function
with a domain of [-1, 1] and a
with a domain of [-1, 1] and a
range of [-π/2, π/2] that
range of [0, π] that satisfies
satisfies the relation sin y = x.
the relation cos y = x.
• If f(x) = sin x and f-1(x) = sin-1 x • If f(x) = cos x and f-1(x) = cos-1 x
(f-1 ◦ f)(x) = x on [-π/2, π/2]
(f-1 ◦ f)(x) = x on [0, π]
and
and
(f ◦ f-1)(x) = x on [-1, 1]
(f ◦ f-1)(x) = x on [-1, 1]
7.2 Inverse Trigonometric Functions
Finding the Domain and Range.
Graph.
Inverse Tangent Function
• The inverse tangent function, • f(x) = 2sin-1 (4x)
denoted y = tan-1 x or
y = arctan x is the function
• g(x) = cos-1 (¾ x) – π
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
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 ( 3 )
• cos-1 ( 3 2 )
• 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].