Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Section 7.2 Right Triangle Trigonometry

Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.

Section 7.2

Right Triangle Trigonometry





Trigonometric Functions of Acute Angles



Find the value of each of the six trigonometric functions of the angle .




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





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



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


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



1Given that cot and is an acute angle, find the exact value of each


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


1Given that cot and is an acute angle, find the exact value of each


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







tan 75(a) (b) cos38 sin 52

cot15

tan 75 tan 75(a) 1

cot15 tan 75

(b) cos38 sin 52 cos38 cos38 0

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Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Section 7.2 Right Triangle Trigonometry