Sat9e ppt 7_2

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 θ.


10 3 10Given sin and cos , find the value of each of the four remaining

10 10trigonometric functions of .

θ θ

θ

= =

10sin 10 10 110tancos 10 33 10 3 10

10

θθθ

= = = × =1 1

cot 31tan3

θθ

= = =

1 1 10csc 10

sin 1 110

0 0θ

θ= = = = 1 1 10 10

seccos 33 10 3 10

10

θθ

= = = =


22

Find the exact value of each expression. Do not use a calculator.

cos1 3(a) cos 35 (b) cotcsc 35 3sin

3

ππ

π+ ° −°

2 2 22

1(a) cos 35 sin 35 cos 35 1

csc 35+ ° = ° + ° =

°

cos3(b) cot cot cot 0

3 3 3sin3

ππ π π

π − = − =


2Given that sin and is an acute angle, find the exact value of each

5of the remaining five trigonometric functions of .

θ θ

θ

=

2sin = so draw a triangle with these sides.

5

b

cθ =

b = 2c = 5

θ

a

2 2 22 5a + =2 25 4 21a = − =

21a =

21cos =

5

a

cθ = 2 2 21

tan = 2121

b

aθ = =

5csc =

2

c

bθ =

5 5 21sec =

2121

c

aθ = =

21cot =

2

a

bθ =

2Given that sin and is an acute angle, find the exact value of each


θ θ

θ

=

2 2sin c 1osθ θ+ =2

22co 1s

5θ + = ÷

2 4 211

2 2cos

5 5θ − ==

21 21

2cos

5 5θ ==

Since θ is acute the trig functions are all positive.

2sin 2 55tancos 52

2 21

21 215

1

θθθ

= = = × =

1 21cot

tan 2θ

θ= = 1 1 5

csc2sin 25

θθ

= = =

1 1 5 5 21sec

cos 21215

21θ

θ= = = =


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


θ θ

θ

=

1cot = so draw a triangle with these sides.

3

a

bθ =

b = 3c

θ

a = 1

2 2 21 3 c+ =2 10c =

10c =

1 10cos =

1010

a

cθ = = 3

tan = 31

b

aθ = =

10csc =

3

c

bθ =

10sec = 10

1

c

aθ = =

3 3 10sin =

1010

b

cθ = =


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


θ θ

θ

=

2 2cot 1 cscθ θ+ =2

211 csc

3θ + = ÷

2 1csc

9

101

9θ = + =

10 10

9csc

3θ ==

Since θ is acute the trig functions are all positive.

sin 3 10 110costan 3 10 3

3 1010

10

θθθ

= = = × =

1 1tan 3

1cot3

θθ

= = =

1 1 3 3 10sin

csc 10103

10θ

θ= = = =

1 1 10sec 10

cos 1 110

0 0θ

θ= = = =


tan 75(a) (b) cos38 sin 52

cot15

° ° − °°

tan 75 tan 75(a) 1

cot15 tan 75

° °= =° °

(b) cos38 sin52 cos38 cos38 0° − ° = ° − ° =

Sat9e ppt 7_2

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