Download Review Problems Multiple Choice - Plane Trigonometry | MATH 111 and more Study notes Trigonometry in PDF only on Docsity!
Please note that NOTA = none of the above
(1) Find z to be the nearest (^10)
of a degree
a) 41.4o^ b) 48.6 o^ c) 36.9 o^ d) 53.1 o^ e) NOTA
(2) Find the length of side p. Round to two places.
a) 4.09 cm b) 4.39 cm c) 5.60 cm d) 3.49 cm e) NOTA
(3) Convert 600 degrees to radians.
a) (^3)
b) (^9)
c) (^9)
d) (^9)
e) NOTA
(4) Convert 4.3 radians to degrees. Round to the nearest degree.
a) 14º b) 774º c) 493º d) 126º e) NOTA
4 cm
3 cm z
p
6 cm
43 o
Math 111 Review Problems Multiple Choice
(5) Find the period of y = −4 cot 2x
a) π b) (^2)
c) 2π d) (^4)
e) NOTA
(6) Find the phase shift of the function y = −4 sin(2πx + π)
a) (^4) − π b) (^2)
c) (^2)
−^1
d) (^4) − π e) 2π
(7) The solutions of cos^2 x – cos x – 2 = 0 are (where k denotes an arbitrary integer)
a) 2kπ b) (^2)
- 2kπ c) π + 2k d) − π + 2kπ e) kπ
(8) The exact value of csc
^
π is
a) 2 b) 23 c) (^2)
d) –2 e) (^3) −^2
(9) An angle measured in standard position has the point (4,5) on its terminal ray. What is cos ( )?θ
a) (^41)
4 b) (^41) − 5 c) (^41)
5 d) (^41) − 4 e) − 54
(10) Simplify the expression 1 cos
1 (^2) a − using fundamental identities. The result is
a) cot 2 a b) sec 2 a c) 0 d) tan 2 α e) NOTA
(11) sec tan^ x x^ −^1 =
2
a) 32 b) 1 c) −^23 d) −^32 e) NOTA
(18) The equation of the graph below is
a) y^ =^2 +^3 cos(^2 x+^2 ) b) y=^1 +^2 cos(^ πx^ +^ π)
c) y^ =^1 +^2 sin(^ πx^ −^ π) d) y=^2 +^3 sin(^2 x−^2 )
e) NOTA
(19) The graph shows y^ =^3 sin(^ Bx+C). B =
a) 1 b) π c) (^2) −^ π d) (^2)
e) 21
(20) Find the equation of the graph
a) y^ =^ tan^ π 2 x b) y^ =tan^4 x
c) y^ =^ tan^2 x d) y^ =^ tan 21 x
(26) A central angle cuts an arc of 45 m in a circle whose radius is 9 m. Find the measure of the angle. Round to one place.
a) 405.0º b) 452.4º c) 286.5º d) 202.5º e) NOTA
Use the following figure for 27 and 28.
(27) Which ratio is equal to sec R?
a) (^) t^ r^ b) (^) m^ r^ c) mt^ d) mr^ e) NOTA
(28) Which ratio is equal to sin M?
a) (^) r
m b) (^) t
m c) (^) t
r d) (^) m
t e) NOTA
For 29, 30 use 3.14 for π. Which of the listed values is NOT coterminal with the given value of x?
(29) x = –4.
a) 14.65 b) –16.75 c) 17.79 d) 20.93 e) NOTA
(30) x = 86.
a) 60.93 b) 48.37 c) 32.67 d) 16.97 e) NOTA
r
t m
M
T
R
For 31 and 32, A is in Quadrant III and sin A = −^53.
(31) Find cos A.
a) (^5)
b) (^5)
c) (^5)
d) (^5)
e) NOTA
(32) Find tan A.
a) (^4)
b) (^4)
c) (^3)
d) (^3)
e) NOTA
(33) Angle B is in standard position in Quadrant II, and sin B = (^58)
3 .
Find a point on the terminal side of angle B.
a) (^3 ,^58 ) b) (3,7) c) (–7,3) d) (7,3) e) NOTA
(34) Angle C is in standard position in quadrant III, and cos C = (^9)
. Find a point on the
terminal side of angle C.
a) (^65 ,^9 ) b) (^ −^65 ,^9 ) c) (^97 ,^9 ) d) (^ −^97 ,^9 ) e) NOTA
(35) Find sin
^
7 π exactly.
a) 3 2
b) 3 2
− (^) c) 2
d) (^2)
e) NOTA
(36) Find cos
^
4 π exactly.
a) 3 2
b) 3 2
− (^) c) 2
d) (^2)
e) NOTA
a) 2π b) 6π c) (^3)
d) π e) NOTA
(43) What is the horizontal shift?
a) 2 left b) 1.5 right c) 2 right d) (^3)
left e) NOTA
(44) If cos m = n and sin m = k, then
a) cos(−m) = −n and sin(−m) = −k b) cos(−m) = n and sin(−m) = k
c) cos(−m) = −n and sin(−m) = k d) cos(−m) = n and sin(−m) = −k
e) NOTA
(45) A cosine function has period 12 and amplitude 8. It is also known that f(5) = 30 is the maximum function value. Find f(11).
a) Not enough information b) 24 c) 22 d) 14 e) NOTA
(46) Find exactly 1 sin 3 2
a) (^3)
π b)
π c) (^3)
d)
− π e) NOTA
(47) Find exactly cos −^1 (−.5).
a) (^6)
− π b) (^6)
π c) (^3)
d) (^3)
π e) NOTA
(48) In ∆ ABC
A = 40 ° a = 2.6m B = 60°
Find b.
a) 3.5m b) 3.9m c) 1.9m d) 2.7m e) NOTA
(49) In ∆ ABC
a = 5 ft b = 3 ft C = 68°
Find c. Round to two places.
a) 45.24 ft b) 22.7 ft c) 6.73 ft d) 4.77 ft e) NOTA
(50) Solve sin x = .5 on [0, 2 π].
a) (^6)
is the only solution b) (^3)
is the only solution
c) (^6)
d) (^3)
π
e) NOTA
(51) What is the range of y = sin x?
a) [−1, 1] b) [0, 2 π] c) [− π π, ] d) (−∞,∞) e) NOTA
(52) What is the range of y = sin −^1 x?
(1) Sketch angles in standard position.
a) −300 degrees
b) 500 degrees
c) 150 degrees
d) 3π
e) (^2)
f) − 3
g) 6
h)
^
−^
cos 1 4
i)
^
−^ −
cos 1 2
j)
^
−^ −
tan 1 5
Math 111 Review Problems Partial Credit Problems
(2) Find x and y.
(3) Find θ andx.
(4) Find α andx.
20 o
y x
70 o
20 cm
25 o
15 cm x
θ
10 cm
For Problems 10, 11, and 12 find one solution analytically, then find other solutions by any method.
(10) 4.4 − 3.2 cos(1.2x) = 5.1 on the interval [0, 10].
(11) 2.7 tan(.2x) = −6.5 on [0, 50].
(12) 500 + 25 sin(.52x) = 512 on [0, 12].
(13) Angle (^3) A =^2 π , and angle A is in standard position. The terminal side of angle A intersects
the unit circle at the point (a, b). Find the exact values of a and b.
(14) Repeat for angle (^6) B =^7 π .
(15) Repeat for angle (^4) C =^5 π .
(16) Find a possible formula for each graph
a) b)
(17) Simplify each expression by writing it without using any trigonometric functions. Find an exact value whenever possible.
a) −^ ^ 6 ^ sin 1 sin^7 π
b) sin(sin −^1 .5)
c) sin(cos −^1 0)
d) sin(cos −^1 x)
e) tan(sin −^1 x)
(18) Find a possible formula for each data table.
a) x (^0 1 2 3 ) y (^6 4 2 4 )
a) On the given axes, make a sketch of y = cos x.
b) Indicate on the graph approximate solutions to cos x = –.
c) For each solution indicate the corresponding quadrant of the unit circle.
(22) Repeat #21 with y = sin x and sin x = –.
(23) A cosine function y^ =^ g x( )has its average value at x^ =^2 and x^ =^10.
a) List three values that could be the period of this function. b) What is the largest possible period for this function? Explain.
