Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Section 7.2 Right Triangle...
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Transcript of Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Section 7.2 Right Triangle...
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Section 7.2
Right Triangle Trigonometry
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Trigonometric Functions of Acute Angles
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Find the value of each of the six trigonometric functions of the angle .
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
10 3 10Given sin and cos , find the value of each of the four remaining
10 10trigonometric functions of .
10sin 10 10 110tancos 10 33 10 3 10
10
1 1
cot 31tan3
1 1 10csc 10
sin 1 110
0 0
1 1 10 10sec
cos 33 10 3 1010
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
22
Find the exact value of each expression. Do not use a calculator.
cos1 3(a) cos 35 (b) cotcsc 35 3sin
3
2 2 22
1(a) cos 35 sin 35 cos 35 1
csc 35
cos3(b) cot cot cot 0
3 3 3sin3
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
2Given that sin and is an acute angle, find the exact value of each
5of the remaining five trigonometric functions of .
2sin = so draw a triangle with these sides.
5
b
c
b = 2c = 5
θ
a
2 2 22 5a 2 25 4 21a
21a
21cos =
5
a
c 2 2 21
tan = 2121
b
a
5csc =
2
c
b
5 5 21sec =
2121
c
a
21cot =
2
a
b
2Given that sin and is an acute angle, find the exact value of each
5of the remaining five trigonometric functions of .
2 2sin c 1os 2
22co 1s
5
2 4 21
12 2
cos5 5
21 21
2cos
5 5
Since θ is acute the trig functions are all positive.
2sin 2 55tancos 52
2 21
21 215
1
1 21cot
tan 2
1 1 5
csc2sin 25
1 1 5 5 21sec
cos 21215
21
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
1Given that cot and is an acute angle, find the exact value of each
3of the remaining five trigonometric functions of .
1cot = so draw a triangle with these sides.
3
a
b
b = 3c
θ
a = 1
2 2 21 3 c 2 10c
10c
1 10cos =
1010
a
c 3
tan = 31
b
a
10csc =
3
c
b
10sec = 10
1
c
a
3 3 10sin =
1010
b
c
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
1Given that cot and is an acute angle, find the exact value of each
3of the remaining five trigonometric functions of .
2 2cot 1 csc 2
211 csc
3
2 1
csc9
101
9
10 10
9csc
3
Since θ is acute the trig functions are all positive.
sin 3 10 110costan 3 10 3
3 1010
10
1 1tan 3
1cot3
1 1 3 3 10sin
csc 10103
10
1 1 10sec 10
cos 1 110
0 0