GRAPH the following functions. Label the vertex and the axis of symmetry. Identify the roots or the yintercepts where necessary. State the Domain and Range.
__________________________________________________________________________________________________
Solve the Quadratics by Factoring.
__________________________________________________________________________________________________
__________________________________________________________________________________________________
Solve the following pairs of systems of equations.
1. 𝑥𝑥 + 𝑦𝑦 = 7, 𝑥𝑥 2 + 𝑦𝑦 2 = 25
2. 𝑦𝑦 = 𝑥𝑥 − 3, 𝑦𝑦 = 𝑥𝑥 2 − 3𝑥𝑥 − 8
3. 𝑦𝑦 = 2 − 𝑥𝑥, 𝑥𝑥 2 − 𝑦𝑦 2 = 8
4. 2𝑥𝑥 + 𝑦𝑦 = 5, 𝑥𝑥 2 + 𝑦𝑦 2 = 25
Find Points A and B.
NAME ______________________________________________ DATE
13-1 Practice
____________ PERIOD _____
(Average)
Right Triangle Trigonometry
Find the values of the six trigonometric functions for angle ␪.
1.
2.
3.
3兹苵
3
␪
␪
5
45
␪
3
11
24
15
1
8
5
4兹6
3
苶
兹苶
sin ␪ ⫽ ᎏᎏ, cos ␪ ⫽ ᎏᎏ,
17
2
17
11
11
2
15
17
11
5兹苶6
兹3
苶
tan ␪ ⫽ ᎏᎏ, csc ␪ ⫽ 2,
tan ␪ ⫽ ᎏᎏ, csc ␪ ⫽ ᎏᎏ, tan ␪ ⫽ ᎏᎏ, csc ␪ ⫽ ᎏᎏ,
8
15
5
24
3
17
8
11兹6
4
2
6
3
苶
兹苶
兹苶
sec ␪ ⫽ ᎏᎏ, cot ␪ ⫽ ᎏᎏ sec ␪ ⫽ ᎏᎏ, cot ␪ ⫽ ᎏᎏ sec ␪ ⫽ ᎏᎏ, cot ␪ ⫽
15
8
5
3
24
sin ␪ ⫽ ᎏᎏ, cos ␪ ⫽ ᎏᎏ, sin ␪ ⫽ ᎏᎏ, cos ␪ ⫽ ᎏᎏ,
兹苶
3
Write an equation involving sin, cos, or tan that can be used to find x. Then solve
the equation. Round measures of sides to the nearest tenth and measures of
angles to the nearest degree.
4.
5.
6.
49⬚
x
x
x
17
30⬚
32
7
x
32
x
7
tan 30⬚ ⫽ ᎏᎏ, x ⬇ 4.0
7.
20⬚
8.
tan 49⬚ ⫽ ᎏᎏ, x ⬇ 14.8
9.
7
x
19.2
x⬚
41⬚
28
17
x
sin 20⬚ ⫽ ᎏᎏ, x ⬇ 10.9
28
x
cos 41⬚ ⫽ ᎏᎏ, x ⬇ 37.1
17
x⬚
15.3
19.2
17
tan x⬚ ⫽ ᎏᎏ, x ⬇ 48
7
15.3
sin x⬚ ⫽ ᎏᎏ, x ⬇ 27
Solve 䉭ABC by using the given measurements. Round measures of
sides to the nearest tenth and measures of angles to the nearest degree.
10. A ⫽ 35⬚, a ⫽ 12
b ⬇ 17.1, c ⬇ 20.9, B ⫽ 55⬚
11. B ⫽ 71⬚, b ⫽ 25
a ⬇ 8.6, c ⬇ 26.4, A ⫽ 19⬚
12. B ⫽ 36⬚, c ⫽ 8
13. a ⫽ 4, b ⫽ 7
14. A ⫽ 17⬚, c ⫽ 3.2
15. b ⫽ 52, c ⫽ 95
a ⬇ 6.5, b ⬇ 4.7, A ⫽ 54⬚
a ⬇ 0.9, b ⬇ 3.1, B ⫽ 73⬚
A
b
C
c
a
B
c ⬇ 8.1, A ⬇ 30⬚, B ⬇ 60⬚
a ⬇ 79.5, A ⬇ 33⬚, B ⬇ 57⬚
16. SURVEYING John stands 150 meters from a water tower and sights the top at an angle
©
Glencoe/McGraw-Hill
778
Glencoe Algebra 2
NAME ______________________________________________ DATE
13-2 Practice
____________ PERIOD _____
(Average)
Angles and Angle Measure
Draw an angle with the given measure in standard position.
1. 210⬚
2. 305⬚
3. 580⬚
y
y
x
O
y
x
O
5. ⫺450⬚
4. 135⬚
y
6. ⫺560⬚
y
x
O
x
O
O
y
x
x
O
Rewrite each degree measure in radians and each radian measure in degrees.
␲
10
␲
30
7. 18⬚ ᎏᎏ
8. 6⬚ ᎏᎏ
2␲
5
41␲
9
11. ⫺72⬚ ⫺ᎏᎏ
12. ⫺820⬚ ⫺ᎏᎏ
15. 4␲ 720⬚
16. ᎏᎏ 450⬚
9␲
2
19. ⫺ᎏᎏ ⫺810⬚
29␲
6
25␲
13. ⫺250⬚ ⫺ᎏᎏ
18
9. 870⬚ ᎏᎏ
5␲
2
13␲
5
13␲
30
17. ᎏᎏ 468⬚
7␲
12
20. ⫺ᎏᎏ ⫺105⬚
347␲
180
11␲
14. ⫺165⬚ ⫺ᎏᎏ
12
10. 347⬚ ᎏᎏ
18. ᎏᎏ 78⬚
3␲
8
21. ⫺ᎏᎏ ⫺67.5⬚
3␲
16
22. ⫺ᎏᎏ ⫺33.75⬚
Find one angle with positive measure and one angle with negative measure
coterminal with each angle. 23–34. Sample answers are given.
23. 65⬚ 425⬚, ⫺295⬚
24. 80⬚ 440⬚, ⫺280⬚
25. 285⬚ 645⬚, ⫺75⬚
26. 110⬚ 470⬚, ⫺250⬚
27. ⫺37⬚ 323⬚, ⫺397⬚
28. ⫺93⬚ 267⬚, ⫺453⬚
2␲ 12␲
5
5
8␲
5
7␲
3␲ ␲
32. ⫺ᎏᎏ ᎏᎏ, ⫺ᎏᎏ
2 2
2
29. ᎏᎏ ᎏᎏ, ⫺ᎏᎏ
5␲ 17␲
6
6
7␲
6
9␲
␲ 7␲
33. ⫺ᎏᎏ ᎏᎏ, ⫺ᎏᎏ
4 4
4
17␲ 29␲
6
6
7␲
6
29␲
5␲ 19␲
34. ⫺ᎏᎏ ᎏᎏ, ⫺ᎏᎏ
12 12
12
30. ᎏᎏ ᎏᎏ, ⫺ᎏᎏ
31. ᎏᎏ ᎏᎏ, ⫺ᎏᎏ
35. TIME Find both the degree and radian measures of the angle through which the hour
5␲
hand on a clock rotates from 5 A.M. to 10 A.M.
⫺150⬚; ⫺ᎏᎏ
6
36. ROTATION A truck with 16-inch radius wheels is driven at 77 feet per second
(52.5 miles per hour). Find the measure of the angle through which a point on the
outside of the wheel travels each second. Round to the nearest degree and nearest radian.
3309⬚/s; 58 radians/s
©
Glencoe/McGraw-Hill
784
Glencoe Algebra 2
UNIT 6 WORKSHEET 7
USING THE UNIT CIRCLE
Use the unit circle above to find the exact value of each of the following. (Exact value means no decimal
approximations.)
2π
=
3
A) tan
π
=
4
B) cos
D) sin
11π
=
6
 2π
E) tan  −
 3
4π
=
3
 11π 
H) cos  −
=
 6 
G) sec
C) cosπ =

=

F) csc
I) sin
π
=
3
13π
=
4
 5π 
J) csc  −
=
 6 
 π
K) tan  −  =
 6
 19π
M) sec  −
 3
N) cot
 9π
P) cos  −
 2
S)

=


=

 7π 
sin  −
 =
6 

L) cot
2π
=
3
π
=
4
O) cot
11π
=
6
Q) sin
21π
=
4
R) cot
7π
=
4
T) cot
26π
=
3
U) cos
π
=
3
V) Find all angles θ in the interval [ 0, 2π ) that satisfy the expression:
sin θ = −
3
2
θ = _____________________
W) Find all angles θ in the interval [ 0, 2π ) that satisfy the expression:
csc θ = 2
θ = _____________________
X) Find all angles θ in the interval [ 0, 2π ) that satisfy the expression:
tan θ = 3
θ = _____________________
Y) Find all angles θ in the interval [ 0, 2π ) that satisfy the expression:
sec θ = undefined
θ = _____________________
UNIT 6 WORKSHEET 4
USING THE UNIT CIRCLE
Use the unit circle above to find the exact value of the six trigonometric functions for each of the
following angles.
A)
3π
4
B) 300°
sin θ =
csc θ =
sin θ =
csc θ =
cos θ =
sec θ =
cos θ =
sec θ =
tan θ =
cot θ =
tan θ =
cot θ =
C) −
5π
6
D)
2π
3
sin θ =
csc θ =
sin θ =
csc θ =
cos θ =
sec θ =
cos θ =
sec θ =
tan θ =
cot θ =
tan θ =
cot θ =
E)
13π
3
F) −240°
sin θ =
csc θ =
sin θ =
csc θ =
cos θ =
sec θ =
cos θ =
sec θ =
tan θ =
cot θ =
tan θ =
cot θ =
G) −
7π
2
H) 135°
sin θ =
csc θ =
sin θ =
csc θ =
cos θ =
sec θ =
cos θ =
sec θ =
tan θ =
cot θ =
tan θ =
cot θ =
I)
13π
6
J) −
2π
3
sin θ =
csc θ =
sin θ =
csc θ =
cos θ =
sec θ =
cos θ =
sec θ =
tan θ =
cot θ =
tan θ =
cot θ =
UNIT 6 WORKSHEET 14
EVALUATING TRIG FUNCTIONS OF ANY ANGLE
Evaluate the six trigonometric functions of the angle θ , in standard position, that has a
terminal side with the following endpoints. (Remember, reference angles are always drawn in relation
to the x axis.)
A)
( 3,5)
B)
( 2, −1)
sin θ =
csc θ =
sin θ =
csc θ =
cos θ =
sec θ =
cos θ =
sec θ =
tan θ =
cot θ =
tan θ =
cot θ =
C)
( −4, 2 )
D)
( −3, −5)
sin θ =
csc θ =
sin θ =
csc θ =
cos θ =
sec θ =
cos θ =
sec θ =
tan θ =
cot θ =
tan θ =
cot θ =
E) (1, −7 )
F)
( −6,1)
sin θ =
csc θ =
sin θ =
csc θ =
cos θ =
sec θ =
cos θ =
sec θ =
tan θ =
cot θ =
tan θ =
cot θ =
1 
G)  ,8 
2 
1 2
H)  , − 
4 5
sin θ =
csc θ =
sin θ =
csc θ =
cos θ =
sec θ =
cos θ =
sec θ =
tan θ =
cot θ =
tan θ =
cot θ =
I)
( −2, −9 )
J)
( −1, 6 )
sin θ =
csc θ =
sin θ =
csc θ =
cos θ =
sec θ =
cos θ =
sec θ =
tan θ =
cot θ =
tan θ =
cot θ =
K)
( 4, −3)
3 4
L)  , 
4 5
sin θ =
csc θ =
sin θ =
csc θ =
cos θ =
sec θ =
cos θ =
sec θ =
tan θ =
cot θ =
tan θ =
cot θ =