This preview shows page 1. Sign up to view the full content.
Unformatted text preview: Trigonometry I Copyright © 2006, Barry Exam
Trigonometry I Standards Test Practice Mabillard. 0 www.math40s.com
www.math40s.com 1. The minimum and the maximum of a trigonometric function are shown in the diagram.
a) Write a cosine equation for the function b) Determine the value of the y – intercept, correct to three decimal places 2. Convert 11π
to degrees
18 Trigonometry I Standards Test Practice Exam 1 www.math40s.com 3. Find the exact value of sinθ if cos θ = 1
, and the terminal arm is in Quadrant I.
7 4. What is the period in the function f ( x ) = 3sin ( 5 x ) − 2 5. Given the point (3, 4), determine the exact values of cosθ and sinθ 6. The length of arc swept out by an angle θ is 50 cm. If the radius of the circle is 18 cm,
determine the measure of θ in radians. Trigonometry I Standards Test Practice Exam 2 www.math40s.com 7. Determine a value for x that would make the function f ( x ) = 3csc x
undefined in the domain [0, 2π ) 8. Determine the value of f (10 ) in the function f ( x ) = 4 sin ⎡π ( x − 2 ) ⎤ + 3
⎣
⎦ 3π ⎞
⎛
9. The graph of y = 6 cos ⎜ x +
⎟ + 1 is illustrated below.
4⎠
⎝
Determine the exact values of g, h, m & n. Trigonometry I Standards Test Practice Exam 3 www.math40s.com 10. If the measure of the central angle is π
4 , determine the measures of the other two angles within the triangle. 11. Determine the number of radians between the hour hand and the minute hand at 7:00. Trigonometry I Standards Test Practice Exam 4 www.math40s.com ⎛ 7π ⎞
12. Determine the value of cos ⎜ −
⎟
⎝ 4⎠ 13. The circle x 2 + y 2 = 1 is drawn below, along with the line y = 3
.
2 Determine the coordinates of the two intersection points. 14. The graph of f ( x ) = 6sin x + d touches the xaxis once (but does not pass through)
on the interval 0 ≤ x ≤ 2π . A possible value for d is: Trigonometry I Standards Test Practice Exam 5 www.math40s.com 15. a) Graph y = cos x b) Graph y = cos −1 x c) State the domain of f −1 ( x ) 16. The maximum point on a trigonometric graph is at the point (4, 6), and the minimum
point is at (2, 2). If the graph is of the form y = a cos ⎡b ( x + c ) ⎤ + d , then determine
⎣
⎦
possible values for each of the parameters. Trigonometry I Standards Test Practice Exam 6 www.math40s.com 17. An angle of 15° is equivalent to _______ radians. (exact value) 5π ⎞
⎛
18. The exact value of cos −1 ⎜ cos
⎟ is
6⎠
⎝ 19. Write the general equation of a vertical asymptote in the graph of y = csc x 20. If csc θ = 2 and tan θ < 0 , determine the value of cos θ Trigonometry I Standards Test Practice Exam 7 www.math40s.com ⎡π
⎤
21. Given the function f ( x ) = 2sin ⎢ ( x − 2 ) ⎥
⎣2
⎦
a) Sketch the graph b) Sketch y = f ( x ) 22. If the coordinates of a point P (θ ) on the unit circle is (a, b), then the coordinates of
the point P ⎡θ + 180o ⎤ are
⎣
⎦ Trigonometry I Standards Test Practice Exam 8 www.math40s.com 23. State the period of the graph of y = csc θ 24. Convert 3π
to degrees. Express answer to one decimal place.
5 25. Given the function f ( x ) = tan x
⎛ π π⎞
a) Sketch y = f ( x ) on the domain ⎜ − , ⎟
⎝ 2 2⎠ b) State the domain of f ( x ) c) Sketch the graph of f −1 ( x ) Trigonometry I Standards Test Practice Exam 9 www.math40s.com 26. A floating ball in a lake goes up and down with the tide.
At 1 second, the ball has a minimum height of 5 cm below surface level.
At 3 seconds, the ball has a maximum height of 5 cm above surface level.
a) Sketch a graph for the first 4 seconds of motion b) Write an equation for the function 27. If the product of cos x and sin x is negative, then which quadrant is the angle in? ⎛1⎞
28. The value of sin −1 ⎜ ⎟ is
⎝2⎠ π⎞
⎛
29. The exact value of sin ⎜ cos ⎟ is
2⎠
⎝ Trigonometry I Standards Test Practice Exam 10 www.math40s.com ⎛1
3⎞
30. If the coordinates of a point P (θ ) on the unit circle are ⎜ , −
⎟ , then the
⎜2
2⎟
⎝
⎠
o
coordinates of the point P ⎡θ + 180 ⎤ are
⎣
⎦ 31. A tire rolls 3π metres while turning 240°. Determine the area of the wheel. Trigonometry I Standards Test Practice Exam 11 www.math40s.com MULTIPLE CHOICE SECTION
1. Given csc θ = 5
, the exact value of tan θ is
4 5
4
3
b)
5 a) 3
4
4
d) ±
3 c) ± π m. The tire is rolled and travels a total distance of 28π m.
5
By the time the tire stops, it has rolled through an angle of
2. A tire has a radius of a) 28π
b) 140°
28
c)
rad
5
d) 8021.41° 3. Given the trigonometric function f ( x ) = cos x , the statement which is true is
a) f ( x) = − f ( x) b) f ( x) = f ( −x) c) f ( x ) = f −1 ( x ) d) f ( x) = − f (−x) 4. If 900 < θ < 1800 , a true statement is
a) 00 < θ < 900
b) cos θ ≤ tan θ
c) 0 < sin θ < 1
d) 0 < cos θ < 1 Trigonometry I Standards Test Practice Exam 12 www.math40s.com 5. Given the function f ( x ) = 12 cos ( 2 x ) , and the transformation g ( x ) =
then the amplitude of g ( x ) is
a)
b)
c)
d) 1
f ( x) ,
4 2
3
4
12 6. The function f ( x ) = 2sec x has a range of
a) ( −2, 2 ) b) ( −∞, −2] ∪ [2, ∞ )
⎡ 1 1⎤
c) ⎢ − , ⎥
⎣ 2 2⎦
d) ( −∞, ∞ ) 7. A wheel turns through an angle of 16 radians. This angle measurement in degrees is
a)
b) π0
8
180 π
c) 8π 0
d) 28000 π 8. A sine function has a range of [6, 2] and a period of 4. A trigonometric equation with
these properties is
⎛π ⎞
a) y = 8 sin ⎜ θ ⎟ + 2
⎝2 ⎠
b) y = 4sin ( 4θ ) − 2
⎛π ⎞
c) y = 4 sin ⎜ θ ⎟ − 2
⎝2 ⎠
⎛2 ⎞
d) y = 4sin ⎜ θ ⎟ − 2
⎝π ⎠ Trigonometry I Standards Test Practice Exam 13 www.math40s.com 9. The angle 24π
is coterminal to an angle of
3 a) 0˚
2π
b)
3
5π
c)
6
7π
d)
3 ⎛ 7π ⎞
10. The exact value of csc ⎜
⎟ is
⎝4⎠
a) − 2
2
b) −
2
2
c)
2
2
d) 11. Given that cos θ =
a)
b)
c)
d) 4
3
and sin θ = − , then the terminal arm is located in quadrant
5
5 I
II
III
IV 12. The period of the function g(x) is 8. If g ( 0 ) = 12, g ( 4 ) = 6, and g ( 8) = 12 , then the
value of g (12 ) is
a)
b)
c)
d) 0
6
12
18 Trigonometry I Standards Test Practice Exam 14 www.math40s.com 13. An angle of 3π
on the unit circle has coordinates of
2 13
,
22
22
b) −
,
22
c) (0, 1)
d) (1, 0) a) 14. If secθ > 0 and sin θ < 0 , then θ terminates in quadrant
a) I
b) II
c) III
d) IV 1
π⎞
⎛
15. The period and phase shift for the trigonometric equation y = sin 4 ⎜ θ − ⎟ are
2
3⎠
⎝
π
a) period = 4 ; phase shift =
left
3
π
b) period = 4 ; phase shift =
right
3
π
π
c) period =
; phase shift =
left
2
3
π
π
d) period =
; phase shift =
right
2
3 16. The equation of an asymptote on the graph of y = csc x is
π
a) x =
4
π
b) x =
2
c) x = π
3π
d) x =
2 Trigonometry I Standards Test Practice Exam 15 www.math40s.com 17. If tan x sin x < 0 , then x terminates in quadrants
a) II or III
b) II or IV
c) I or IV
d) III or IV ⎛ 2⎞
18. The value of sin −1 ⎜
⎜ 2 ⎟ is:
⎟
⎝
⎠
π
a)
4
5π
b)
4
4π
c)
3
11π
d)
6 Trigonometry I Standards Test Practice Exam 16 www.math40s.com ...
View
Full
Document
This note was uploaded on 02/09/2011 for the course 168 comm 168 taught by Professor Kiscabean during the Winter '10 term at UCLA.
 Winter '10
 KISCABEAN

Click to edit the document details