PreCal Final
The graph of f(x) = secs undergoes these transformations: a reflection about the x-axis and a horiztonal shrink with a factor of 1/2. Which graph shows the transformed function?
A
Which of the following statements is impossible? A: 3sinX = -5 B: 224tanX=225 C: 5cosX = -4 D: cosA+sinB = 1.99
A: 3sinX = -5
Find the exact value of tan30 A: √3/3 B: √3 C:√3/2 D:3
A: √3/3
Which graph illustrates an even function?
B
Evaluate log5(25)/log5(4) A: 20 B: 5 C: 2 D: 1
C: 2
Which of the following curves has the shortest period? A: y = 4sinX B: y = -3sin(1/2x-10°) C: y = -6cos(4/3x) D: y = 10sin(3/4x)
C: y = -6cos(4/3x)
The periodic function in the graph below is A: y = 3cosx B: y = 2cos3x C: y = 3cos2x D: y = 3cos(1/2)x
C: y = 3cos2x
Which graph represents f(x) = lx-1l+3
D
Which of the following cannot be calculated? I) tan90 II) csc180 III) cot0 A: I B: II C: I and II D: I, II, and III
D: I, II, and III
If 0≤x<360, which of the following is a solution to the equation 2cotX-1=0? A: x = 60 B: x=60 or x=120 C: x=60 or x=240 D: x=60 or x=300
D: x = 60 or x = 300
Which graph represents the function f(x) = [x] on the interval -5≤x≤-2?
A
What are the roots of this equation? x^3-4x-8=-2x^2 A: -2, 2 B: -2, 4 C: -4, 1, 2 D: -4, 2, 4
A: -2,2
Which of the following is a solution to sin(x√2)=1? A: -7π/2√2 B: -π/2√2 C: π/2 D: 11π/2
A: -7π/2√2
A particle is traveling with harmonic motion with the following positions p at the given times t. Determine the position p at time t=57 A: 177 B: 9.8 C: 6.3 D: 14.2
A: 177
In triangle ABC, if B=25°, b=9, and c=11. How many triangles are possible? A: 2 triangles B: 1 triangle C: no triangles D: infinite triangles
A: 2 triangles
In right triangle ABC, A=20°, and the hypotenuse AB has length 7. Find side BC. A: 2.39 B: 2.55 C: 6.58 D: 20.47
A: 2.39
In triangle ABC, a=5.0, b=2.0, and C=80°, find c to the nearest tenth A: 5.1 B: 5.4 C: 5.6 D: 5.8
A: 5.1
A hot air balloon is hovering over a field. Person A looks E and sees the balloon at an angle of elevation 22°, Person B looks W and sees the balloon at an angle of elevation 44°. If A and B are 2000 ft apart, find the height of the balloon A: 570 B: 820 C: 792 D: 307
A: 570 ft
If a wheel with radius 3 inches is rotating at 180°/sec, then the linear velocity of a point on the rim is A: 9.42 in/sec B: 0.95 in/sec C: 1.05 in/sec D: 28.27 in/se
A: 9.42 in/sec
The angle of depression from the top of a cliff 600 feet high to the ground floor of a house is 33°40'. To the nearest foot, how far is the house from the base of the cliff? A: 901 B: 400 C: 1082 D: 333
A: 901
What are the solutions to the equation x^4-7x^3+11x^2-7x+10=0 A: x = 2, 5, i, -i B: x = -1, 2, 5 C: x= -5, -2, i, -i D: x= -1, 1, 2, 5
A: x= 2, 5, i, -i
What is the phase shift for f(x)=5sin(x-π/3)+2? A: π/3 to the right B: π/3 to the left C: 5π/3 to the right D: 5π/3 to the left
A: π/3 the right
This graph shows a function f(x) for x≤0 If f(x) is an odd function, what is the graph of f(x) for x≥0?
B
If cosT = 1/3 and angle T is in quadrant IV, then sin T = A: -2/3 B: (-2√2)/3 C:-√2/3 D:±(2√2)/3
B: (-2√2)/3
sin225 + tan45 = A: (2+√2)/4 B: (2-√2)/2 C: 1+√3/2 D: 1-√2
B: (2-√2)/2
What are the points of intersection of the graphs of the equations x^2+y^2 = 16 and x^2-y^2 = 2? A: (4,√2), (-4,√2), (4,-√2), (-4,-√2) B: (3,√7), (-3,√7), (3,-√7), (-3,-√7) C: (√7,3), (-√7,3), (√7,-3), (-√7,-3) D: (16,2), (-16,2), (16,-2), (-16,-2)
B: (3,√7), (-3,√7), (3,-√7), (-3,-√7)
Find the exact value of cot120 A: -√3 B: - (√3/3) C: -(√3/2) D: -(√2/2)
B: -(√3/3)
FInd the exact value of cos225 A: 2 B: -√2/2 C: √2/2 D:1/2
B: -√2/2
Find sin29°42' to four decimal places A: .4894 B: .4955 C: .4890 D: .4912
B: .4955
Find sec17°8'49" to four decimal places A: .9556 B: 1.0465 C: 3.3919 D: 1.0460
B: 1.0465
The first term in an infinite geometric sequence is 12 and the sum of the sequence in 15. What is the common ratio? A: -1/5 B: 1/5 C: 4/5 D: 9/5
B: 1/5
Going from A to B, a ship travels on bearing S28°15' E. If the ship returns from B to A, its heading is A: 28°15' B: 118°15' C: 151°45' D: 331°45'
B: 118°15'
In triangle ABC, a=5, b=7, and c=6. Find the area of the triangle to the nearest whole number A: 14 B: 15 C: 16 D: 17
B: 15
Find, in degrees, the measure of a 3/4 counterclockwise rotation? A: 135 B: 270 C: -135 D: -270
B: 270
In the figure above, find the most accurate value of X to the nearest meter A: 39 B: 40 C: 35 D: 66
B: 40
Find the phase shift of y = 2-2sin(2/3x+30°) A: 45 right B: 45 left C: 10 right D: 10 left
B: 45° left
Which of the following measurements is different from the others? A: 120 rpm B: 4πft/sec C: 720°/hr D: 12 radians/5 min
B: 4πft/sec
In triangle ABC, if A=102°, a=5, and b=2, find C to the nearest degree A: 23 B:55 C:62 D:triangle doesn't exist
B: 55°
Which of the following statements would give the largest value of X if X was less than 90? A: 7sinX=4 B: 5cosX=2 C: 4tanX=6 D: 8cscX=10
B: 5cosX=2
The beacon of a lighthouse swings through an arc of 55°. If the beam of light can be seen from 6.5 miles away, what arc length does the path of the beam travel to the nearest mile? A: 358 B: 6 C: 8 D: 12
B: 6 miles
From the window in my house, 25 ft high, I see a tree across the street. From the window, the angle of depression of the base of the tree is 21° and the angle of elevation of the top of the tree is 31°. Find the height of the tree A: 39 ft B: 64 ft C: 36 ft D: 60 ft
B: 64 ft
Which of the following gives the value for cos64cos12+sin65sin12? A: cos77 B: cos53 C: sin53 D: sin77
B: cos53
Which of the following is not equal to 1? A: sin ²x+cos ²x B: sin³xcotxsecx C: (tanx-secx)(tanx+secx) D: all are
B: sin³XcotXsecX
If cosA=cosB, then does A=B? A: always B: sometimes C: never D: impossible to determine
B: sometimes
Which of the following measurements is different from the others? A: 10 rpm B: πft/sec C: 1°/hr D: 1/5min
B: πft/sec
Which expression is equal to cos(x-5π/6)? A: 1/2(cosx-√3sinx) B: 1/2(sinx-√3cosx) C: -1/2(√3cosx+sinx) D: -1/2(√3sinx+cosx)
B:1/2(sinx-√3cosx)
This graph results from which sequence of transformation of the graph f(x)=sinx? A: a reflection across the x-axis, a vertical shift up 1/2 unit, and a horizontal stretch by a factor of 3/2 B: a reflection across the x-axis, a vertical shift up 1/2 unit, and a horizontal shrink by a factor of 2/3 C: a vertical shift down 1/2 unit, and a horizontal stretch by a factor of 3/2 D: a vertical shift down 1/2 unit, and a horizontal shrink by a factor of 2/3
B:a reflection across the x-axis, a vertical shift up 1/2 unit, and a horizontal shrink by a factor of 2/3
What is the amplitude of the periodic function shown in this graph?
C
Which graph best represents y = cos^-1X?
C
Which graph represents f(x) 2+tanx
C
Which graph represents this piecewise function?
C
What could be the terminal points of a 585° angle drawn in standard position? A: (√3/2, -1/2) B: (-√3/2, -1/2) C: (-1/2, -1/2) D: (-√3/2, 1/2)
C: (-1/2, -1/2)
What could be the terminal points of a 480° angle drawn in standard position? A: (√3/2, 1/2) B: (-√3/2, 1/2) C: (-1/2, √3/2) D: (√3/2, -1/2)
C: (-1/2, √3/2)
Which expression can be written as x^4y^6, provided x.y ≠0? A: (x^4y^3)^2/x^2 B: x^3y^5/xy C: (xy)^6/x^2 D: (x^2y^3)^4/(xy)^2
C: (xy)^6/x^2
cos330-sin315 = A: √3 B: (√3+2)/2 C: (√3 +√2)/2 D: (√3-√2)/2
C: (√3+√2)/2
Find, in degrees. the measure of 2/3 clockwise rotation A: 135 B: -120 C: -240 D: -270
C: -240°
If cosX=3/5, X in quadrant IV, find tan2X A: 3/4 B: -3/4 C: -4/3 D: 4/3
C: -4/3
The amount of water required to fill three small cylinders, each of a different size, is equal to the amount of water required to fill a large cylinder. The volumes of the 4 cylinders with x as their radii are given in this table... Which is the best approximation of the radius, in units, of each cylinder? A: 1.000 B: 1.750 C: 1.839 D: 1.892
C: 1.839
Which of the following statements is impossible A: 8cosX = -8 B: 4tanX = 125 C: 100secX = 99 D: 12cotX = 1
C: 100secX=99
Change 5π/8 into degrees A: 120 B: 135 C: 112.5 D: 5/16
C: 112.5°
The radius of a circle is 3.6 cm. The length of the arc of the circle cut by a central angle is 8.4 cm. Find the measurement of the central angle A: 2.3 B: 124.1 C: 133.7 D: 172.8
C: 133.7°
Going from A to B, a plane travels on a heading of 200°, if the plane returns from B to A, its heading is A: 340° B: 70° C: 20° D: 160°
C: 20°
In the right triangle ABC, one leg is 12, while the hypotenuse is 13. What is the measurement of the smallest angle to the nearest degree? A: 67 B: 30 C: 23 D:18
C: 23°
To the nearest hundredth of a square foot, what is the area of this triangle? A: 2.8 B: 3.98 C: 4.15 D: 8.29
C: 4.15
In triangle ABC, A=32°, B=71°. and a=5.0. Find b to the nearest tenth. A: 8.0 B: 8.7 C: 8.9 D: 9.2
C: 8.9
The graph of f(x) = √x undergoes these transformations A reflection across the x-axis A vertical stretch by a factor of 5 A horizontal shift of 1/3 unit to the right A vertical shift of 1/2 unit down A: f(x)= 5√(x+1/3)-1/2 B: f(x)= 5√(x-1/3)+1/2 C: f(x)= -5√(x-1/3)-1/2 D: f(x)= 5√(x+1/3)+1/2
C: f(x)= -5√(x-1/3)-1/2
In triangle ABC, B=65°, b=2, and c=12. How many triangles are possible? A: 2 B: 1 C: none D: infinite
C: no triangles
Which of the following is not equal to sinX? A: cosx/cotx B: cscx-cotxcosx C: sin2x/sinx D: all are
C: sin2X/sinX
To find the distance from point B to point A on an island, a surveyor made the measurements shown below. Find the distance AB to the nearest tenth of a meter. A: 26.4 B: 25.0 C: 18.7 D: 26
D. 26.0
These statements are true for the function f(x) = x^5-x^3+7x-35:... Which interval must contain a real root of this function? A: (1.93, 1.94) B: (1.93, 1.95) C: (1.94, 1.95) D: (1.95, 1.96)
D: (1.95, 1.96)
What angle is co-terminal with 172° A: 18 B: -172 C: 432 D: -188
D: -188°
If sinX = 4/5, X in quadrant II, find cos 2X A: 3/5 B: -6/5 C: -12/25 D: -7/25
D: -7/25
Completely simplify x²•x²/x A: 0 B: 1 C: x D: 1/x
D: 1/x
If the sides of a triangular piece of land measures 120 ft, 85 ft, and 197 ft, the smallest angle of the triangle is approximately A: 10.9 B: 43.7 C: 25.3 D: 13.4
D: 13.4°
Find the phase shift of y=3+cos(1/2x-20°) A: 10 left B: 10 right C: 40 left D: 40 right
D: 40 right
Which of the following is not a measure of angular velocity? A: 45 rpm B: 5°/sec C: 12π/hr D: 4 inch/radian
D: 4inch/radian
What is the value of tan^-1(-√3)? A: π/3 B: π/2 C: 7π/3 D: 5π/3
D: 5π/3
What is the equation in general form of this hyperbola? x²/4 - y²/9 = 1 A: 9x²-4y ²+1 =0 B: 9x²-4y ²+36 =0 C: 9x²-4y ²-1 =0 D: 9x²-4y ²-36 =0
D: 9x²-4y ²- 36= 0)
Which of the following is a solution to cos² x+cosx=0? I: x=90 II: x=180 III: x=270 A: I only B: I and II only C: II and III only D: I, II, and III
D: I, II, and III
Which of the following is solution to the equation 2sin²x+sinx=1? I: x = 30 II: x = 150 III: x = 270 A: III B: I and III C: II and III D: I, II, and III
D: I, II, and III
Which statement about the graph of this relation is true? {(-1,0), (0,1), (0,-1), (1,0)} A: It is symmetric only with respect to the x-axis B: It is symmetric only with respect to the y-axis C: It it symmetric with respect to the x-axis, y-axis, but not the origin D: It is symmetric with respect to the x-axis, y-axis, and origin
D: It is symmetric with respect to the x-axis, y-axis, and origin
Which of the following is the range of y = 1-3sin(2x-30°)? A: [0°, 180°] B: [-3,3] C: [-2,2] D: [-2,4]
D: [-2,4]
Which of the following is not an equation for the graph above? A: y = 1-2cos2x B: y =1+2cos2(x-90°) C: y = 1+2sin2(x-45°) D: all are
D: all are
Which of the following is not equal to cosx? A: sinx/tanx B: =√1-sin²x C: 1/secx D: all are
D: all are
If sinX = -5/13, X is in quadrant III, which of the following has the largest value? A: cosX B: secX C: tanX D: cotX
D: cotX
If sinX = -8/17, X in quadrant III, which of the following has the largest value? A: cosX B: secX C: tanX D: cotX
D: cotX
Which equation, if true, shows that the graph of f(x)=x²+5 is symmetric about the y-axis? A: f(x) = (1/x)²+5 B: f(x) = √x²+5 C: f(x) = x²-5 D: f(x) = (-x)²+5
D: f(x) = (-x)²+5
In triangle ABC, if C = 121°, b = 2, and a = 3, to find c, you would use A: pythagorean theorem B: basic trig function C: law of sines D: law of cosines
D: law of cosines
In triangle ABC, if C=96°, b=20, and c=15, to find B, you would use A: law of cosines B: law of sines C: basic trig functions D: none would help
D: none would help
Point P (x,y) is on the terminal side of an angle X in the standard position. P is located "r" units from the origin. Tell which statement is false. A: sinX = y/r B: cosX = x/r C: cotX = x/y D: secX = r/y
D: secX = r/y
In triangle ABC, if a = 51, b = 22, c =84, to find A, you should use A: basic trig functions B: law of sines C: law of cosines D:triangle is impossible
D: triangle is impossible
Which of the following curves has the longest period? A: y = 2cosX B: y = 4sin(1/3x) C: y = 5cos(4x) D: y = -2sin(1/10x-10°)
D: y = -2sin(1/10x-10°)