Review Problems Exam for Plane Trigonometry | MATH 111, Study notes of Trigonometry

Download Review Problems Exam for 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 1 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 10 b) 9 28 c) 9 26 d) 9 32 e) NOTA (4) Convert 4.3 radians to degrees. Round to the nearest degree. a) 14º b) 774º c) 493º d) 126º e) NOTA (5) Find the period of y = −4 cot 2x a) π b) 2  c) 2π d) 4  e) NOTA 4 cm 3 cm z p 6 cm 43o Math 111 Review Problems Multiple Choice (6) Find the phase shift of the function y = −4 sin(2πx + π) a) 4   b) 2 1 c) 2 1  d) 4   e) 2π (7) The solutions of cos2x – 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        3  is a) 2 b) 2 3 c) 2 1  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) 5 4  (10) Simplify the expression 1 cos 1 2  a using fundamental identities. The result is a) a2cot b) a2sec c) 0 d) 2tan e) NOTA (11)   x x tan 1sec2 a) 1 b) tan x c) x3tan d) cot x e) x2cot (12) Given that 2 3 cos  and θ)? is acute, what is value of θ)?? a) 30º b) 45º c) 60º d) 15º e) –30º a) xy 2 tan   b) xy 4tan c) xy 2tan d) xy 2 1 tan e) NOTA (21) Given the figure, find x a) 12 b) 40 c) 20 d) 48 e) 36 (22) A central angle of 63º is in a circle of radius 18cm. How long is the arc cut by the angle? Round to 2 places. a) 19.79 cm b) 9.90 cm c) 39.58 cm d) 79.16 cm e) NOTA (23) A pole casts a 10 foot shadow. A man who is 6 feet tall casts a 3.5 foot shadow. How tall is the pole? 24 20 10 x  a) 5.83 ft b) 2.10 ft c) 17.14 ft d) 21.00 ft e) NOTA (24) Tim is 4’3” tall, and his brother Tom is 5’9”. If Tim casts a 9 foot shadow, how long of a shadow will Tom cast? a) 6.65 ft b) 12.18 ft c) 2.71 ft d) 24.44 ft e) NOTA (25) A central angle of 70 degrees cuts an arc of 6 feet. Find the radius of the circle. a) 6 ft b) 5.14 ft c) 9.82 ft d) 12 ft e) NOTA (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) t m d) r m 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? r t r m M T R (29) x = –4.19 a) 14.65 b) –16.75 c) 17.79 d) 20.93 e) NOTA (30) x = 86.05 a) 60.93 b) 48.37 c) 32.67 d) 16.97 e) NOTA For 31 and 32, A is in Quadrant III and sin A = 5 3  . (31) Find cos A. a) 5 4  b) 5 4 c) 5 3 d) 5 3  e) NOTA (32) Find tan A. a) 4 3 b) 4 3  c) 3 4 d) 3 4  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)  58,3 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 4 . Find a point on the terminal side of angle C. a)  9,65 b)  9,65 c)  9,97 d)  9,97 e) NOTA (35) Find sin       6 7 exactly. a) 3 2 b) 3 2  c) 2 1  d) 2 1 e) NOTA 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, 2π]. a) 6  is the only solution b) 3  is the only solution c) 6  , 6 5 d) 3  , 2 3  e) NOTA (51) What is the range of y = sin x ? a) [−1, 1] b) [0, 2π] c) [−π, π] d) (−∞,∞) e) NOTA (52) What is the range of y = sin−1 x? a) [0, 2π] b) [−1, 1] c) [0, π] d)        2 , 2  e) NOTA (53) What is the range of y = tan−1 x? a) (−∞,∞) b) [0, 2π] c) [0, π] d)        2 , 2  e) NOTA (54) y = g(x) is periodic with period 5; g(6.1) = 9.7. Find g(21.1). a) 5 b) 6.1 c) 9.7 d) 24.7 e) NOTA (55) A cosine function has period 12 and its maximum value at x = 5. At what x value will the function have a minimum? a) 8 b) 11 c) 14 d) 17 e) NOTA (56) A tangent function has period 16, a horizontal intercept at x = 9, and no vertical shift. At what x value will the graph of this function have a vertical asymptote? a) 13 b) 17 c) 21 d) 25 e) NOTA (1) Sketch angles in standard position. a) −300 degrees b) 500 degrees c) 150 degrees d) 3π e) 2 3 f) −3 g) 6 h)       5 4 cos 1 i)        3 2 cos 1 j)        3 5 tan 1 (2) Find x and y. Math 111 Review Problems Partial Credit Problems (14) Repeat for angle 6 7 B . (15) Repeat for angle 4 5 C . (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 7 sinsin 1  b) sin(sin−1.5) c) sin(cos−10) d) sin(cos−1x) e) tan(sin−1x) (18) Find a possible formula for each data table. a) x 0 1 2 3 4 y 6 4 2 4 6 b) x  0  2 y Undefined 0 Undefined 0 c) x -1 -0.5 0 0.5 1 1.5 y -10 -7 -10 -13 -10 -7 (19) A sine function ( )y f x has a period of 8 and amplitude of 3. It is also known that (2) 18f  is a minimum value of the function. a) Find the maximum value of the function. b) List three values for x that produce a maximum value. c) List three values for x that product the average value of the function. d) Write an equation for this function. (20) Solve each triangle ABC, if possible. If there is no such triangle, explain how you know. If two triangles are possible, solve both. a) a = 5 cm, b = 6 cm, c = 7 cm b) a = 6.17 in, b = 11.52 in, c = 17.41 in c) a = 5 ft, b = 7 ft, C = 78 deg d) a = 10 m, b = 6 m, B = 25 deg e) a = 5 cm, b = 6 cm, B = 35 deg f) A = 40 deg, B = 50 deg, c = 6 ft (21) a) On the given axes, make a sketch of y = cos x. b) Indicate on the graph approximate solutions to cos x = –.4 c) For each solution indicate the corresponding quadrant of the unit circle. (22) Repeat #21 with y = sin x and sin x = –.7 (23) A cosine function ( )y g x has its average value at 2x  and 10x  .