Precalculus_review For The Final
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PRECALCULUS. FINAL EXAM REVIEW. 1. Use the given values and trigonometric identities to evaluate (if possible) the other trigonometric functions. tanѲ = 3/2, secѲ = √13/2 2. Use the fundamental identities to simplify the trig. Expressions a) Tan 2 Ѳ (csc2 Ѳ – 1) b) sin(-x) cot x Sin(π/2 – x) 1. Verify the identity a) Cot2x – cos2x = cot2xcos2x b) sin2x + sin2(π/2 – x) = 1 1. Estimate the angle to the nearest one-half radian
2. Given
b) Determine the quadrant in which the angle lies. List one positive and one negative coterminal angle for
Find the complement(if it is possible) and the supplement of 2π/21
7.
complement_________ supplement__________
Convert 1.5 from radians to degrees.
_________
8. Convert 280°8’50’’ to decimal degree form. Round your answer to two decimal places. 9. Find the radian measure of the central angle of a circle with a radius of intercept an arc of length 25 ft. __________
12 feet that
10. Find the length of the arc on a circle with a radius of 20 meters intercepted by a central angle of 138° ________ 11.
A 10 inch radius lawn roller makes 1.2 rev per sec. a) Find the angular speed.
_________
b) Find the speed of the tractor that is pulling the roller _________ 12. Find the point (x,y) on the circle that corresponds to real number t=5π/6
_________
13. For t=2π evaluate(if it is possible the six trig. Functions Sin_____ cos_____ tan____ cot_____ sec____ csc_____ 14. Use a calculator to evaluate the trig function cos 5π/3. Round to two decimal places _________
15. Given the triangle ABC. Find the exact values of the six trig functions B
sin________ cos________
10 C
Tan________ 12
A
cot________ Sec________ Csc______
16. Use trig identities to transform one side into the other cscX tanX = secX B
17. Find the altitude of the given triangle.
B
12 m
505
A
C
18. Find the domain, range, period, amplitude, period, zeros, asymptotes, and shifts of the following trig functions. Graph them . a) y = 3 sin x
b) y = -1/2 cos π x - 3
domain:________
domain:_________
range:_________
range:___________
amplitude:______
amplitude:________
period:_________
period:_________
shifts:__________
shifts:__________
zeros:__________
zeros:__________
asymptotes:______
asymptotes:________
19. Find a, b, c, and d for y = asin(bx-c) + d and y = acos(bx-c) + d that match the graph below. Write the functions.
Sin; a=___ b=____ c=_____ d=_____,
y=________________________
Cos; a=___ b=____ c=_____ d=_____,
y=________________________
20. Find the domain, range, period, zeros, asymptotes, and shifts of the following trig functions. Sketch the graph the functions. a) y = tan(x + π/4)
b) y = ½ cot(x - π/2)
domain:________
domain:_________
range:_________
range:___________
period:_________
period:_________
shifts:__________
shifts:__________
zeros:__________
zeros:__________
asymptotes:______
asymptotes:________
21. Given; y=1/2cos(∏x - 1), determine a. Domain: b. Range c. Amplitude d. Period 22. Describe the relationship between the graphs of
e. Phase shift
f. Graph
f(x) = sinx and g(x) = 3sin(2x + 1). 23. Consider the angle 5π/4 radians a. Sketch the angle in standard position. b. Determine two coterminal angles(one positive and one negative) c. Convert the angle to degree measure. 24. A truck is moving at a rate of 90 km/h, and the diameter of its wheels is 1 meter . Find the angular speed of the wheels in radians per min. 25. Use trigonometric identities to transform one side of the equation into the other. a) cscxtanx = secx b) cotx + tanx = sec2x cotx 26. Find the exact values of the six trigonometric functions of the angle shown in the fig.
27.Find the six trig. Functions of the angle(in standard position) whose terminal side passes through the given point a) (12,16)
b) (4,-8)
Extra credit (x,4x) x rel="nofollow">0
28. Find the remaining 5 trig functions a) sec x = 6/5, tanx<0
b) cos x =-2/3,
sin x >0
29. Evaluate without using a calculator a) tan π/3
b) sec 270
30. Use a calculator a) tan 33
b) sin(-π/9)
31. Find the reference angle a) 264
b) 635
c) -6π/5
32. Perform the indicated operations and write the result in standard form.
(4-√-9)(2+√-9) 33. Write 3+i in standard form. 1- i 34. Plot 6 - 5i and -3 + 2i in the complex plane. 35.Write as a product of linear factors. f(x)= x4 - 16 36. Find the 3rd degree polynomial with integer coeficients that has 2, 3+i, and 3-i zeros. 37. Use the x = 2i to find the zeros of f(x) = x4 - x3- 2x2- 4x - 24. 38. Find the vertical and horizontal asymptotes of the following functions. a) f(x) = 3 + x x b) f(x) = x 4 - x2 c) f(x) = 3x2- x x3- x d) f(x) = x3- x2+ 1 x e) f(x) = 3x + 2 5 - 2x 39. Graph f(x)=(x-4)2-4 and f(x)=x2-4 on the same coordinate plane(use graph paper, be accurate that the vertex, x and y intercepts could be perfectly seen). Describe how each graph differs from the graph of g(x)=x2 40. List all the possible rational zeros of the functions a) f(x)=x4-x3-2x2 b) g(x)=t4-4t2 41. Perform the indicated operation a) (7+5i)+(-4+2i) b) (4-i)2-(4+i)2
c) 3+2i 5+i 42. Find a polynomial function with integer coefficients that has the given zeros a) -2, -2, -5i b) 1, -4, -3+5i 43. Sketch the graph of the rational functions. As a sketching aid, check for domain, x and y intercepts, vertical, horizontal and slant assymptotes. a) f(x)= 2x3 b) g(x)= 5x c) z(x)=2x2+7x+3 2 2 x +1 x -4 x+1 44. Find the balance in an account at the end of 12 years if $6500.00 is invested at an interest rate of 8% compound continuously. A=Pert 45.Write 3-4= 1/81 in logarithmic form 46.Evaluate log 125 47.Solve Log572 – log5x = 3log52
48.Sketch the graph of y = log2(x + 1) of base formula
**Extra Credit Sketch y> log2(x + 1) Find the value of log423.9 using the change
49.Solve 5x+2 = 87 using common logarithms 50.Given that log 4 = 0.6021, evaluate log 40,000 51.Convert log7235 to a natural logarithm and evaluate 52.Evaluate Ln(1/0.45) Use trigonomtric identities to transform one side of the equation into the other. 53. sinx = cosx tanx 54. sec2x - tan2x = 1 55. sin2x + cos2x = cos2x tan2x + 1 56. (secx - tanx)(1+ sinx) = cosx 57.Find the six trig. functions of the angle(in standard position) whose terminal side passes through the given point a) (12,16) b) (4,-8) 58. Find the remaining 5 trig functions a) sec x = 6/5, tanx<0
Extra credit (x,4x) x>0
b) cos x =-2/3,
sin x >0
59. Evaluate without using a calculator a) tan π/3
b) sec 270
60. Use a calculator a) tan 33
b) sin(-π/9)
61. Find the reference angle a) 264
b) 635
c) -6π/5
2. Given
b) Determine the quadrant in which the angle lies. List one positive and one negative coterminal angle for
Find the complement(if it is possible) and the supplement of 2π/21
7.
complement_________ supplement__________
Convert 1.5 from radians to degrees.
_________
8. Convert 280°8’50’’ to decimal degree form. Round your answer to two decimal places. 9. Find the radian measure of the central angle of a circle with a radius of intercept an arc of length 25 ft. __________
12 feet that
10. Find the length of the arc on a circle with a radius of 20 meters intercepted by a central angle of 138° ________ 11.
A 10 inch radius lawn roller makes 1.2 rev per sec. a) Find the angular speed.
_________
b) Find the speed of the tractor that is pulling the roller _________ 12. Find the point (x,y) on the circle that corresponds to real number t=5π/6
_________
13. For t=2π evaluate(if it is possible the six trig. Functions Sin_____ cos_____ tan____ cot_____ sec____ csc_____ 14. Use a calculator to evaluate the trig function cos 5π/3. Round to two decimal places _________
15. Given the triangle ABC. Find the exact values of the six trig functions B
sin________ cos________
10 C
Tan________ 12
A
cot________ Sec________ Csc______
16. Use trig identities to transform one side into the other cscX tanX = secX B
17. Find the altitude of the given triangle.
B
12 m
505
A
C
18. Find the domain, range, period, amplitude, period, zeros, asymptotes, and shifts of the following trig functions. Graph them . a) y = 3 sin x
b) y = -1/2 cos π x - 3
domain:________
domain:_________
range:_________
range:___________
amplitude:______
amplitude:________
period:_________
period:_________
shifts:__________
shifts:__________
zeros:__________
zeros:__________
asymptotes:______
asymptotes:________
19. Find a, b, c, and d for y = asin(bx-c) + d and y = acos(bx-c) + d that match the graph below. Write the functions.
Sin; a=___ b=____ c=_____ d=_____,
y=________________________
Cos; a=___ b=____ c=_____ d=_____,
y=________________________
20. Find the domain, range, period, zeros, asymptotes, and shifts of the following trig functions. Sketch the graph the functions. a) y = tan(x + π/4)
b) y = ½ cot(x - π/2)
domain:________
domain:_________
range:_________
range:___________
period:_________
period:_________
shifts:__________
shifts:__________
zeros:__________
zeros:__________
asymptotes:______
asymptotes:________
21. Given; y=1/2cos(∏x - 1), determine a. Domain: b. Range c. Amplitude d. Period 22. Describe the relationship between the graphs of
e. Phase shift
f. Graph
f(x) = sinx and g(x) = 3sin(2x + 1). 23. Consider the angle 5π/4 radians a. Sketch the angle in standard position. b. Determine two coterminal angles(one positive and one negative) c. Convert the angle to degree measure. 24. A truck is moving at a rate of 90 km/h, and the diameter of its wheels is 1 meter . Find the angular speed of the wheels in radians per min. 25. Use trigonometric identities to transform one side of the equation into the other. a) cscxtanx = secx b) cotx + tanx = sec2x cotx 26. Find the exact values of the six trigonometric functions of the angle shown in the fig.
27.Find the six trig. Functions of the angle(in standard position) whose terminal side passes through the given point a) (12,16)
b) (4,-8)
Extra credit (x,4x) x rel="nofollow">0
28. Find the remaining 5 trig functions a) sec x = 6/5, tanx<0
b) cos x =-2/3,
sin x >0
29. Evaluate without using a calculator a) tan π/3
b) sec 270
30. Use a calculator a) tan 33
b) sin(-π/9)
31. Find the reference angle a) 264
b) 635
c) -6π/5
32. Perform the indicated operations and write the result in standard form.
(4-√-9)(2+√-9) 33. Write 3+i in standard form. 1- i 34. Plot 6 - 5i and -3 + 2i in the complex plane. 35.Write as a product of linear factors. f(x)= x4 - 16 36. Find the 3rd degree polynomial with integer coeficients that has 2, 3+i, and 3-i zeros. 37. Use the x = 2i to find the zeros of f(x) = x4 - x3- 2x2- 4x - 24. 38. Find the vertical and horizontal asymptotes of the following functions. a) f(x) = 3 + x x b) f(x) = x 4 - x2 c) f(x) = 3x2- x x3- x d) f(x) = x3- x2+ 1 x e) f(x) = 3x + 2 5 - 2x 39. Graph f(x)=(x-4)2-4 and f(x)=x2-4 on the same coordinate plane(use graph paper, be accurate that the vertex, x and y intercepts could be perfectly seen). Describe how each graph differs from the graph of g(x)=x2 40. List all the possible rational zeros of the functions a) f(x)=x4-x3-2x2 b) g(x)=t4-4t2 41. Perform the indicated operation a) (7+5i)+(-4+2i) b) (4-i)2-(4+i)2
c) 3+2i 5+i 42. Find a polynomial function with integer coefficients that has the given zeros a) -2, -2, -5i b) 1, -4, -3+5i 43. Sketch the graph of the rational functions. As a sketching aid, check for domain, x and y intercepts, vertical, horizontal and slant assymptotes. a) f(x)= 2x3 b) g(x)= 5x c) z(x)=2x2+7x+3 2 2 x +1 x -4 x+1 44. Find the balance in an account at the end of 12 years if $6500.00 is invested at an interest rate of 8% compound continuously. A=Pert 45.Write 3-4= 1/81 in logarithmic form 46.Evaluate log 125 47.Solve Log572 – log5x = 3log52
48.Sketch the graph of y = log2(x + 1) of base formula
**Extra Credit Sketch y> log2(x + 1) Find the value of log423.9 using the change
49.Solve 5x+2 = 87 using common logarithms 50.Given that log 4 = 0.6021, evaluate log 40,000 51.Convert log7235 to a natural logarithm and evaluate 52.Evaluate Ln(1/0.45) Use trigonomtric identities to transform one side of the equation into the other. 53. sinx = cosx tanx 54. sec2x - tan2x = 1 55. sin2x + cos2x = cos2x tan2x + 1 56. (secx - tanx)(1+ sinx) = cosx 57.Find the six trig. functions of the angle(in standard position) whose terminal side passes through the given point a) (12,16) b) (4,-8) 58. Find the remaining 5 trig functions a) sec x = 6/5, tanx<0
Extra credit (x,4x) x>0
b) cos x =-2/3,
sin x >0
59. Evaluate without using a calculator a) tan π/3
b) sec 270
60. Use a calculator a) tan 33
b) sin(-π/9)
61. Find the reference angle a) 264
b) 635
c) -6π/5
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