James Madison High School Trigonometric Ratios and Functions Exercises

Hello thanks in advance ! 20 questions I will upload some of the questions and will add the rest later

Question 1 (5 points)
(0.1)
90°
13
2
V22
120°
135°
√3 1
2.2
150°
12 / 2
60°
V2 2
22
45°C
30°
(-1,0) 180°
0° / 360° |(1,0)
13 1210°
330%
13
2
2
2
2.
2 225°
3150
300°
v 2
2 2
2
240°
3
2
270°
(0.-1)
Using the unit circle, determine the value of sin(-240°).
A) –
B) –
C)
D)
Question 2 (5 points)
The function y= sin 2 (x – 1/2) has a period of
A) 2n.
o
B) “/2.
C) n.
D) 41.
Question 3 (5 points)
Which of the following graphs represents the function y= 2 cos(x – 1/2) – 1?
4 y
A)
2
-2
-TT
25
371
-2
4 y
B)
MA
-27
-2
o
C)
4 y
2
27
HAY
D)
2
x
-25
-TT
T
2TT
31
-2
Question 4 (5 points)
P
Which of the following is true of the angle shown?
A) The angle can be measured in radians only.
B) The terminal side of the angle lies in quadrant II.
C) The measure of the angle is greater than 360°.
D) The angle is not in standard position.
Question 5 (5 points)
Which equations represent two vertical asymptotes of the function y= 3 cot(4/3+)?
A) x= _31/8 and x =
31/8
B) x = 0 and x =
31/8
C) x= – 31/4 and x =
31/4
D) x = 0 and x =
31/4
Question 6 (5 points)
Simplify the expression using trigonometric identities: sec (-0) – cos O.
A) -tan o sin e
B) tan . sin e
C) tan(-0) · sin (-0)
D) tan(-6) · sin e
Question 7 (5 points)
Which of the following are maximum and minimum points of the function y= 2 cos x
– 1?
A) Maximums: (0, 3), (2, 3); Minimum: (1, -3)
B) Maximums: (0, 3), (21, 3); Minimum: (1, -1)
C) Maximums: (0, 1), (21, 1); Minimum: (1, -3)
D) Maximums: (0, 1) (“/2, 1); Minimum: (37/2, -3)
Question 8 (5 points)
(0.1)
90°
600
13
22
2 2
120°
22
135°
3
22 150°
2 2
2
45
30°
NW
(-1,0) 180°
0° / 360°|(1,0)
210°
2
NI-
225
2 2
2 2
330° 3 1
22
3150
2 2
2 2
1 13
240°
300°
270°
(0.-1)
Using the unit circle, determine the value of cos(-150°).
,
A)
O
B) TO
SIA
C)-
D) –
Question 9 (5 points)
Find the period of the function y= 3/2 tan(1/34.
A) 1/6
B) 35
Ос) л
D) 1/3
Question 10 (5 points)
5.5
50°
х
Determine the value of x using a trigonometric ratio.
A) 4.21 units
B) 7.18 units
C) 50.23 units
D) 8.56 units
Question 11 (5 points)
Given that sec = -5/4 and is in quadrant II, find cot e.
A) -4/3
B) -3/5
C) -3/4
D) 413
Question 12 (5 points)
For an angle to be in standard position, its vertex is at the origin and the initial side
lies on the
A) positive y-axis.
B) negative x-axis.
C) negative x-axis.
D) positive x-axis.
Question 13 (5 points)
X
35°
25
Determine the value of x.
A) 35.54
B) 17.51
C) 54.45
D) 16.32
Question 14 (5 points)
Which of the following are maximum and minimum points of the function y= sin(x +
T)?
A) Minimum: (+/4, – 1); Maximum: (57/4, 1)
B) Maximum: (“/2, 1); Minimum: (37/2, -1)
C) Minimum: (“/4, 1); Maximum: (57/4, -1)
OD) Maximum: (1/2, – 1); Minimum: (31/2, 1)
Question 1 (5 points)
(0.1)
90°
13
2
V22
120°
135°
√3 1
2.2
150°
12 / 2
60°
V2 2
22
45°C
30°
(-1,0) 180°
0° / 360° |(1,0)
13 1210°
330%
13
2
2
2
2.
2 225°
3150
300°
v 2
2 2
2
240°
3
2
270°
(0.-1)
Using the unit circle, determine the value of sin(-240°).
A) –
B) –
C)
D)
Question 2 (5 points)
The function y= sin 2 (x – 1/2) has a period of
A) 2n.
o
B) “/2.
C) n.
D) 41.
Question 3 (5 points)
Which of the following graphs represents the function y= 2 cos(x – 1/2) – 1?
4 y
A)
2
-2
-TT
25
371
-2
4 y
B)
MA
-27
-2
o
C)
4 y
2
27
HAY
D)
2
x
-25
-TT
T
2TT
31
-2
Question 4 (5 points)
P
Which of the following is true of the angle shown?
A) The angle can be measured in radians only.
B) The terminal side of the angle lies in quadrant II.
C) The measure of the angle is greater than 360°.
D) The angle is not in standard position.
Question 5 (5 points)
Which equations represent two vertical asymptotes of the function y= 3 cot(4/3+)?
A) x= _31/8 and x =
31/8
B) x = 0 and x =
31/8
C) x= – 31/4 and x =
31/4
D) x = 0 and x =
31/4
Question 6 (5 points)
Simplify the expression using trigonometric identities: sec (-0) – cos O.
A) -tan o sin e
B) tan . sin e
C) tan(-0) · sin (-0)
D) tan(-6) · sin e
Question 7 (5 points)
Which of the following are maximum and minimum points of the function y= 2 cos x
– 1?
A) Maximums: (0, 3), (2, 3); Minimum: (1, -3)
B) Maximums: (0, 3), (21, 3); Minimum: (1, -1)
C) Maximums: (0, 1), (21, 1); Minimum: (1, -3)
D) Maximums: (0, 1) (“/2, 1); Minimum: (37/2, -3)
Question 8 (5 points)
(0.1)
90°
600
13
22
2 2
120°
22
135°
3
22 150°
2 2
2
45
30°
NW
(-1,0) 180°
0° / 360°|(1,0)
210°
2
NI-
225
2 2
2 2
330° 3 1
22
3150
2 2
2 2
1 13
240°
300°
270°
(0.-1)
Using the unit circle, determine the value of cos(-150°).
,
A)
O
B) TO
SIA
C)-
D) –
Question 9 (5 points)
Find the period of the function y= 3/2 tan(1/34.
A) 1/6
B) 35
Ос) л
D) 1/3
Question 10 (5 points)
5.5
50°
х
Determine the value of x using a trigonometric ratio.
A) 4.21 units
B) 7.18 units
C) 50.23 units
D) 8.56 units
Question 11 (5 points)
Given that sec = -5/4 and is in quadrant II, find cot e.
A) -4/3
B) -3/5
C) -3/4
D) 413
Question 12 (5 points)
For an angle to be in standard position, its vertex is at the origin and the initial side
lies on the
A) positive y-axis.
B) negative x-axis.
C) negative x-axis.
D) positive x-axis.
Question 13 (5 points)
X
35°
25
Determine the value of x.
A) 35.54
B) 17.51
C) 54.45
D) 16.32
Question 14 (5 points)
Which of the following are maximum and minimum points of the function y= sin(x +
T)?
A) Minimum: (+/4, – 1); Maximum: (57/4, 1)
B) Maximum: (“/2, 1); Minimum: (37/2, -1)
C) Minimum: (“/4, 1); Maximum: (57/4, -1)
OD) Maximum: (1/2, – 1); Minimum: (31/2, 1)