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°)