PRECALCULUS FINAL EXAM REVIEW

Transcription

1 PRECALCULUS FINAL EXAM REVIEW Evaluate the function at the indicated value of. Round our result to three decimal places.. f () 4(5 ); 0.8. f () e ; 0.78 Use the graph of f to describe the transformation that ields the graph of g. 3. f () 4, g() f (), g() Use the One-to-One Propert to solve the equation for e 57 e 5

2 Write the eponential equation in logarithmic form e Evaluate the function at the indicated value of without using a calculator. 9. f () log ; log 4 ; 4 Use the One-to-One Propert to solve the equation for.. log 4 ( 7) log 4 4. The antler spread a (in inches) and shoulder height h (in inches) of an adult male American elk are related b the model h 6log(a 40) 76. Approimate the shoulder height of a male American elk with an antler spread of 55 inches.

3 Use the properties of logarithms to epand the epression as a sum, difference, and/or constant multiple of logarithms. (Assume all variables are positive.) 6 3. log 3 4. ln z 3 Condense the epression to the logarithm of a single quantit log 8( 4) 7log ln( ) ln( ) 3ln Solve for. When necessar, approimate our result to three decimal places log 4 9. e 4 e

4 . Consider the angle 4π 3 a. Sketch the angle in standard position. b. Determine the quadrant in which the angle lies. c. Determine one positive and one negative coterminal angles.. Consider the angle 80. a. Sketch the angle in standard position. b. Determine the quadrant in which the angle lies. c. Determine one positive and one negative coterminal angles. Convert the angle measure from degrees to radians. If necessar, round our answer to three decimal places

5 Convert the angle measure from radians to degrees. If necessar, round our answer to three decimal places. 4. 7π 6 5. π 3 Evaluate the sine, cosine, and tangent of the angle without using a calculator. 6. π π o o

6 30. Find the length of the arc on a circle with a radius of 0 inches intercepted b a central angle of 45. Find the point (, ) on the unit circle that corresponds to the real number t. 3. t 5π 4 3. t π 3 Evaluate (if possible) the si trigonometric functions of the real number. 33. t 5π t 5π 3 Evaluate the trigonometric function using its period as an aid. 35. sin 7π cos 9π 6

7 Use a calculator to evaluate the trigonometric function. Round our answer to four decimal places. 37. tan30 o 38. csc 3π 5 Find the eact values of the si trigonometric functions of the angle θ shown in the figure θ θ Use the given function value and trigonometric identities (including the cofunction identities) to find the indicated trigonometric functions. 4. cscθ 3 3, secθ 3 a. sinθ b. cosθ c. tanθ d. sec(90 θ)

8 4. John wants to measure the height of a tree. He walks eactl 00 feet from the base of the tree and looks up. The angle from the ground to the top of the tree is 33º. How tall is the tree? 43. An airplane is fling at a height of miles above the ground. The distance along the ground from the airplane to the airport is 5 miles. What is the angle of depression from the airplane to the airport? State the quadrant in which θ lies. 44. tanθ < 0 and cosθ < cosθ > 0 and cscθ < 0

9 Find the values of the si trigonometric functions of θ. 46. cosθ 3, θ lies in Quadrant II sinθ 5, cosθ > You accidentall threw our football on top of a building. From a distance 0 feet awa, the angle of elevation to the roof is 56. How tall is the building?

10 Match the function with its graph. State the amplitude (if it applies) and the period of the function. A csc D tan( π ) B sin E sin( π ) C cot F csc(3)

11 55. Sound waves can be modeled b sine functions of the form a sin b, where is measured in seconds. a. Write an equation of a sound wave whose amplitude is and whose period is second. 64 b. What is the frequenc of the sound wave described in part (a)? True or False? Determine whether the statement is true or false. Justif our answer. 56. The graph of csc can be obtained on a calculator b graphing the reciprocal of sin. 57. The function given b cos has an amplitude that is twice that of the function given b cos. 58. The graph of the function given b f ( ) sin( π ) translates the graph of f ( ) sin eactl one period to the right so that the two graphs look identical.

12 Evaluate the epression without a calculator. 59. arcsin 60. arccos0 6. tan ( 3) 6. arcsin 63. tan cos Evaluate the epression. Round our answer to two decimal places. 65. arcsin cos 0.3

13 Find the eact value of the epression. 67. cos arctan csc arctan 69. Your football landed at the edge of the roof of our school building. When ou are 5 feet from the base of the building, the angle of elevation to our football field is. How high off the ground is our football? 70. A plane is 80 miles south and 95 miles east of Cleveland Hopkins International Airport. What bearing should be taken to fl directl to the airport?

14 Use the Law of Sines to solve (if possible) the triangle. If two solutions eist, find both. Round our answers to two decimal places. 7. B 7o, C 8 o, b A 95o, B 45 o, c 04.8 Find the area of the triangle having the indicated angle and sides. 73. A 7o, b 5, c C 3o, a 6, b From a certain distance, the angle of elevation to the top of a building is 7º. At a point 50 meters closer to the building, the angle of elevation is 3º. Approimate the height of the building.

15 Use the Law of Cosines to solve the triangle. Round our answers to two decimal places. 76. a 5, b 8, c a.5, b 5.0, c The lengths of the diagonals of a parallelogram are 0 feet and 6 feet. Find the lengths of the sides of the parallelogram if the diagonals intersect at an angle of 8º. Use Heron s Area Formula to find the area of the triangle. 79. a 4, b 5, c a.3, b 5.8, c 3.7

16 Determine whether each ordered pair is a solution of the sstem of equations. 8. 3, ), 3 ) ), ( ) 3 ) ( 0, ) 4 d c b a Solve the sstem b graphing Solve each sstem b substitution z z z

17 Solve the sstem b elimination z z z

18 Set up and solve the sstem using a method of our choice. 89. The weekl rentals for a newl released DVD of an animated film at a local video store decreased each week. At the same time, the weekl rentals for a newl released DVD of a horror film increased each week. Models that approimate the weekl rentals R for each DVD are R R 4 8 where represents the number of weeks each DVD was in the store, with corresponding to the first week. a) After how man weeks will the rentals for the two movies be equal? 90. The perimeter of a rectangle is 80 centimeters and the width is 0 centimeters less than the length. Find the dimensions of the rectangle. 9. At a local high school cit championship basketball game, 435 tickets were sold. A student admission ticket cost $.50 and an adult admission ticket cost $5.00. The sum of all the total ticket receipts for the basketball game were $ How man of each tpe of ticket were sold?

19 6 9. Write the first five terms of the sequence a n. (Assume that n begins with ) n 93. Write an epression for the nth term of the sequence:,,7,4, 3, Find the net three terms of the series. Then find the fifth partial sum of the series The sith term of an arithmetic sequence is 65, and the second term is 93. Find the a formula for the nth term. n 96. Write the first five terms of the sequence a 6 ( 3 ). (Assume that n begins with ) n

20 Find the sum ( i i 3 4 ) ( 4 n ) n 99. i 3 i Determine whether the sequence is arithmetic. If so, find the common difference ,,5,9,4, , 3,,, 3,...

21 0. In the first two trips baling ha around a large field, a farmer obtains 3 bales and bales, respectivel. Because each round gets shorter, the farmer estimates that the same pattern will continue. Estimate the total number of bales made if the farmer takes another si trips around the field. Determine whether the sequence is geometric. If so, find the common ratio , 8, 6,, ,5,7,9,,... Write an epression for the nth term of the geometric sequence. Then find the 0 th term of the sequence. 05. a 00, r a, a 3