Convert the angle to radians. Leave as a multiple of π. 1) 36 1) 2) 510 2) 4) )

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1 MAC Review for Eam Name Convert the angle to radians. Leave as a multiple of. ) 6 ) ) 50 ) Convert the degree measure to radians, correct to four decimal places. Use.6 for. ) 0 9 ) ) 0.0 ) Convert the radian measure to degrees. Give answer using decimal degrees to the nearest tenth. 5) -.8 5) Find two real numbers between - and that determine the point on the unit circle. 6) 6) Find the measures of two angles, one positive and one negative, that are coterminal with the given angle. 7) 6 5 7) Find the supplement or complement. 8) Supplement of 8) 9) Complement of 9) Find the eact value for the epression. 0) sin 5 0) ) cos - 5 ) ) tan - )

2 Find the function value using a calculator set in RADIAN mode. Round the answer to four decimal places, where approimate. ) sin 6 7 ) ) cos.08 ) 5) tan.5 5) Complete the table. Round answers to two decimal places. Distance, s 6) (arc length) Radius, r Angle, θ d d 6) 7) Distance, s (arc length) Radius, r Angle, θ 8 ft 5 7) Find the length of an arc intercepted b a central angle θ in a circle of radius r. Round our answer to decimal place. 8) r =.76 cm.; θ = 8 radians 8) 7 9) r = 6.0 in.; θ = 5 9) Determine the measure of the central angle (in radians) given the length of the intercepted arc and the radius. Round answer to decimal places if necessar. 0) Radius = 9 ft; Arc length = 6. ft 0) Solve the problem. ) A biccle with a 8-inch wheel (diameter) travels a distance of 00 feet. How man revolutions does the wheel make (to the nearest revolution)? ) ) A car wheel has a -inch radius. Through what angle (to the nearest tenth of a degree) does the wheel turn when the car rolls forward ft? ) ) A wheel with a 6-inch radius is marked at two points on the rim. The distance between the marks along the wheel is found to be 9 inches. What is the angle (to the nearest tenth of a degree) between the radii to the two marks? ) ) A wheel with a 9-inch diameter is turning at the rate of 9 revolutions per minute. To the nearest inch, what is the speed of a point on the rim in in./min? ) Solve. 5) A wheel is rotating at radians/sec, and the wheel has a 9-inch diameter. To the nearest foot per minute, what is the linear speed of a point on the rim? 5)

3 Solve the problem. 6) Each tire of an automobile has a radius of.5 feet. How man revolutions per minute (rpm) does a tire make when the automobile is traveling at a speed of 7 feet/sec? Round our answer to the nearest tenth. 6) 7) Two wheels are rotating in such a wa that the rotation of the smaller wheel causes the larger wheel to rotate. The radius of the smaller wheel is.6 centimeters and the radius of the larger wheel is 9. centimeters. Through how man degrees will the larger wheel rotate if the smaller one rotates 0? 7) Find the eact value of s in the given interval that has the given circular function value. 8), ; tan s = - 8) 9), ; cos s = - 9) Answer the question. 0) The numbers θ and -θ determine the points A and B, respectivel, on the unit circle. How are the points A and B related? 0) ) The numbers θ and + θ determine the points A and B, respectivel, on the unit circle. How are the points A and B related? ) Graph each using translations or reflections. ) = -sin(-) )

4 ) = -cos(-) ) ) = tan(-) ) ) = sin + 5)

5 6) = cos + 6) Graph the function on the indicated interval. 7) = sin. Graph on [-, ] 7) ) = cos. Graph on [-, ] 8)

6 Match the function with its graph. 9) ) = tan ) = cot ) = -tan ) = -cot 9) A) B) C) D) A) A, B, C, D B) C, A, B, D C)A, D, C, B D) B, D, C, A 6

7 0) ) = sec ) = csc ) = -sec ) = -csc 0) A) B) C) D) A) A, D, C, B B) C, A, B, D C)B, D, C, A D) A, B, C, D ) Find the amplitude, the period, the phase shift and give the equation of the center line for the following trigonometric function. ) = sin Find the amplitude, period and phase shift and the equation of the center line. ) Find the period of = - cos ) Solve the problem. ) Suppose that the average monthl low temperatures for a small town are shown in the table. Month Temperature ( F) ) Model this data using f() = a sin(b( - c)) + d. 7

8 Answer Ke Testname: EREV.0 ) 5 ) 7 6 ) 5.99 ) ) -0. 6), -5 7) 6 5 ; - 5 8) 9) 6 0) - ) - ) ) 0.9 ) ) ) ).0 ft 8) 5.8 cm 9).6 in. 0).6 radians ) 50 revolutions ).6 ).9 ) 95 in./min 5) 9 ft/min 6) 6.7 rpm 7) ) s = 6 9) s = 5 6 0) B is the reflection of A about the -ais. ) B is the reflection of A through the origin. 8

9 Answer Ke Testname: EREV.0 ) ) )

10 Answer Ke Testname: EREV.0 5) ) )

11 Answer Ke Testname: EREV.0 8) ) B 0) B ) amplitude: ; period: /5; phase shift: /0 units to the right; center line = - ) Amplitude: - = ; Period = ; Phase shift: 6 units to the left; Equation of center line: = 5. ) f() = sin (- ) + 6