This document contains content on right triangle trigonometry from a Prentice Hall textbook. It provides examples of using trigonometric functions like sine, cosine, and tangent to solve for missing side lengths or angle measures in right triangles when one of the trig functions is given. It also gives practice problems finding all six trig functions given one is known for an acute angle. The content is copyrighted material from the textbook.

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

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

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

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

5. Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Trigonometric Functions of Acute Angles

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

7. Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Find the value of each of the six trigonometric functions of
the angle θ.

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

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

10. Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
10 3 10
Given sin and cos , find the value of each of the four remaining
10 10
trigonometric functions of .
θ θ
θ
= =
10
sin 10 10 110tan
cos 10 33 10 3 10
10
θ
θ
θ
= = = × =
1 1
cot 3
1tan
3
θ
θ
= = =
1 1 10
csc 10
sin 1 1
10
0 0
θ
θ
= = = =
1 1 10 10
sec
cos 33 10 3 10
10
θ
θ
= = = =

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

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

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

14. Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
2
2
Find the exact value of each expression. Do not use a calculator.
cos
1 3(a) cos 35 (b) cot
csc 35 3sin
3
π
π
π
+ ° −
°
2 2 2
2
1
(a) cos 35 sin 35 cos 35 1
csc 35
+ ° = °+ ° =
°
cos
3(b) cot cot cot 0
3 3 3sin
3
π
π π π
π
− = − =

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

16. Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
2
Given that sin and is an acute angle, find the exact value of each
5
of the remaining five trigonometric functions of .
θ θ
θ
=
2
sin = so draw a triangle with these sides.
5
b
c
θ =
b = 2
c = 5
θ
a
2 2 2
2 5a + =
2
25 4 21a = − =
21a =
21
cos =
5
a
c
θ =
2 2 21
tan =
2121
b
a
θ = =
5
csc =
2
c
b
θ =
5 5 21
sec =
2121
c
a
θ = =
21
cot =
2
a
b
θ =

17. 2
Given that sin and is an acute angle, find the exact value of each
5
of the remaining five trigonometric functions of .
θ θ
θ
=
2 2
sin c 1osθ θ+ =
2
22
co 1s
5
θ
 
+ = ÷
 
2 4 21
1
2 2
cos
5 5
θ − ==
21 21
2
cos
5 5
θ ==
Since θ is acute the trig
functions are all positive.
2
sin 2 55tan
cos 52
2 21
21 21
5
1
θ
θ
θ
= = = × =
1 21
cot
tan 2
θ
θ
= =
1 1 5
csc
2sin 2
5
θ
θ
= = =
1 1 5 5 21
sec
cos 2121
5
21
θ
θ
= = = =

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

19. Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
1
Given that cot and is an acute angle, find the exact value of each
3
of the remaining five trigonometric functions of .
θ θ
θ
=
1
cot = so draw a triangle with these sides.
3
a
b
θ =
b = 3
c
θ
a = 1
2 2 2
1 3 c+ =
2
10c =
10c =
1 10
cos =
1010
a
c
θ = =
3
tan = 3
1
b
a
θ = =
10
csc =
3
c
b
θ =
10
sec = 10
1
c
a
θ = =
3 3 10
sin =
1010
b
c
θ = =

20. Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
1
Given that cot and is an acute angle, find the exact value of each
3
of the remaining five trigonometric functions of .
θ θ
θ
=
2 2
cot 1 cscθ θ+ =
2
21
1 csc
3
θ
 
+ = ÷
 
2 1
csc
9
10
1
9
θ = + =
10 10
9
csc
3
θ ==
Since θ is acute the trig
functions are all positive.
sin 3 10 110cos
tan 3 10 3
3 10
10
10
θ
θ
θ
= = = × =
1 1
tan 3
1cot
3
θ
θ
= = =
1 1 3 3 10
sin
csc 1010
3
10
θ
θ
= = = =
1 1 10
sec 10
cos 1 1
10
0 0
θ
θ
= = = =

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

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

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

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

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

26. Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
tan 75
(a) (b) cos38 sin52
cot15
°
°− °
°
tan 75 tan 75
(a) 1
cot15 tan 75
° °
= =
° °
(b) cos38 sin52 cos38 cos38 0°− ° = °− ° =