class work 1.find the exact value of cot 330 2. find sin2x, cos2x, and tan2x given tan x = -3/2 and...
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Class Work
1. Find the exact value of cot 330
2. Find sin2x, cos2x, and tan2x given tan x = -3/2 and 90 < x< 180
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Class Work
3. Find and 180 < x < 2702
sin sin2 3
ugiven u
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Section 7.4Inverse Trigonometric Functions
Objectives:•To define the inverse of the sine, cosine, and tangent functions.•To understand the domain and range of the inverse trig functions.
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Inverse Sine FunctionThe inverse of the function sin is the function
sin–1 defined by: sin–1x = y sin y = xfor –1 ≤ x ≤ 1 and –π/2 ≤ y ≤ π/2.
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Example 1. Find the exact value of the expression if it is defined:
(a)sin–1 ½
(b)sin–1 (–½)
(c)sin–1 (3/2)
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Class Work Find the exact value of the expression if it is
defined:4.
5.
1 2sin
2
1 5sin4
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Inverse Cosine FunctionThe inverse cosine function is the function cos–1 with domain [–1, 1] and range [0, π], defined by:
cos–1 x = y cos y = x
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Ex 2. Find the exact value of the expression if it is defined:
(a) cos–1
b) cos–1 0
c) cos–1 (5/7)
( 3 / 2)
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Class WorkFind the exact value of the expression if it is
defined:6.
7.
1 2cos
2
1cos ( 1)
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Inverse Tangent FunctionThe inverse tangent function is the function tan–1 with domain and range (–π/2, π/2) defined by:
tan–1 x = y tan y = x
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Ex 3. Find the exact value of the expression if it is defined:
(a)tan–1 1
(b)tan–1
(c)tan–1(–20)
3
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Class WorkFind the exact value of the expression if it is
defined:
8.
9.
1tan ( 1)
1 3tan
3
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Ex 4. Find the exact value of the expression, if it is defined.
a.)
b.)
c.)
1sin (sin )4
1tan(tan 5)
1cos cos3
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Class WorkFind the exact value of the expression, if it is
defined.
10.
11.
1sin sin6
1 2tan tan
3
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Ex 5. Find the exact value of the expression, if it is defined.
a.)
b.)
c.)
1 2sin cos
3
1 1tan sin2
1 5sin cos
6
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Class Work
Find the exact value of the expression, if it is defined.
12.
13.
1 1tan sin2
1 3cos sin
4
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HW#4 p557 1,4,6,7,10,11,13,16,18,
21,26,53,54