1.1 Find the measures of two angles, one positive and one negative, that are coterminal with the given angle. 1) 162

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1 Math 00 Midterm Review Dugopolski Trigonometr Edition, Chapter and. Find the measures of two angles, one positive and one negative, that are coterminal with the given angle. ) ) - ) For the given angle, name the quadrant in which the terminal side lies. ) 5 5) -8 Find the angle of smallest possible positive measure that is coterminal with the given angle. ) -7 7) Convert the angle to decimal degrees and round to the nearest hundredth of a degree. 8) 75 58''' Convert the angle to degrees, minutes, and seconds. 9) -7. Perform the calculation. Epress the answer in degree-minutes-seconds format. 0) ' - 5 0' Find the degree measure of the angle α in the figure. ) 0 ' 9". Convert the angle to radians. Leave as a multiple of. ) -5

2 Convert the degree measure to radian measure. Use the value of found on a calculator and round answers to three decimal places. ).7 ) 8'7'' Convert the radian measure to degree measure. Use the value of found on a calculator and round answers to two decimal places. 5) 7 0 ) Find the measures of two angles, one positive and one negative, that are coterminal with the given angle. 7) 5 For the given angle, name the quadrant in which the terminal side lies. 8) -8 9) 7 0) 7. Draw the angle in standard position. ) ) 7 ) - 7 Find the measure in radians of the smallest possible angle that is coterminal with the given angle. For angles given in terms of, epress the answer in terms of. Otherwise, round to the nearest hundredth. ) 5 7 Perform the indicated operation. 5) - +

3 Find the length of the arc intercepted b the given central angle α in a circle of radius r. ) α = 5, r =. m Find the radius of a circle with central angle α intercepting an arc of length s. 7) α =.5 radians, s = 9 in. Find the area of a sector with the given central angle α in a circle of radius r. 8) α = 90, r = 8 cm Solve the problem. 9) The minute hand of a clock is 7 inches long. What distance does its tip move in 9 minutes?. Solve. 0) An engine is "turning over" at an angular velocit of 00 rpm. Epress this angular velocit in rad/min. Solve the problem. ) A pulle of radius 7 cm rotates 9 times in sec. Find the angular velocit of the pulle. ) A wheel is rotating at radians/sec, and the wheel has a 7-inch diameter. To the nearest foot per minute, what is the linear velocit of a point on the rim? ) A wheel with a 5-inch diameter is turning at the rate of 8 revolutions per minute. To the nearest inch per minute, what is the linear velocit of a point on the rim?. Given that α is an angle in standard position whose terminal side contains the given point, provide the eact value of the indicated function. ) (, 8); cos α 5) (5, ); sin α ) (-7, 5) Find tan α. Find the eact value of the following epression without using a calculator. 7) sin 5 8) cos 9) tan 0) sec

4 ) sec 0 Find the eact value of the epression. sin (5/) ) cos (5/) ) cos - Use a calculator to find the function value to four decimal places. ) cos (.7 ) 5) sin(.) Find the eact value of the epression. Do not use a calculator. ) cos θ, if θ = 5 8 7) tan α, if sin α = - 5 and cos α < 0 Find the quadrant that contains the terminal side of angle α. 8) csc α > 0 and sec α > 0 9) cos α > 0 and csc α < 0 50) csc α < 0 and cot α > 0.5 Solve the problem. 5) Find the acute angle α (in degrees) that satisfies the equation α = sin -. Evaluate each epression without using a calculator. Give the result in degrees. 5) sin - 5) cos - 5) csc - (-) 55) tan - Use a calculator to find the acute angle α (to the nearest tenth of a degree) that satisfies the equation. 5) sin α =

5 57) α = cos - ( ) Evaluate the function requested. Write our answer as a fraction in lowest terms. 58) Find sin α ) Find tan α ) Find cos β. 7 0 Solve the right triangle with the given sides and angles. ) a =.0, β = 8. ) β =., c =. Solve the problem. ) The angle of elevation from a point on the ground to the top of a tower is 8 9'. The angle of elevation from a point feet farther back from the tower is 7 '. Find the height of the tower (to the nearest foot). ) When sitting atop a tree and looking down at his pal Joe, the angle of depression of Mack's line of sight is 9'. If Joe is known to be standing feet from the base of the tree, how tall is the tree (to the nearest foot)? 5) The chairlift at a ski resort has a vertical rise of 00 feet. If the length of the ride is.8 miles, what is the average angle of elevation of the lift (to the nearest tenth of a degree)?. Solve the problem. ) Find sin (α), given that cos (α) = 7 and α is in quadrant IV. 5

6 7) Find sin (α), given that cos (α) = and sin (α) > 0. 7 Draw the angle having the given radian measure. 8) 9) ) - 5 Find the reference angle for the given angle. 7) 7) - Use reference angles to find the eact value of the epression. 7) sin 5 7) tan -5 75) tan 750

7 7) csc - Determine if the equation is true or false. 77) sin ( ) = sin ( ) 78) sin 7 9 = sin Solve. 79) The ferris wheel at an amusement park is 7 ft in diameter, turns at a rate of 7 rpm, and is ft off the ground at the low point. What is the height of a passenger 0 seconds into the ride?. Find the eact value of the trigonometric function. 80) sin 5 8) cos - 5 8) tan - 8) sec 8) csc 85) cot - Solve the problem. 8) Find the coordinates of (/, -5) after it is moved / units to the left. 87) Find the coordinates of (, -8) after it is moved / units to the right and units upward. Determine the midpoint that lies between the two given points. 88) (8, ) and (, 9) 7

8 Determine the coordinates of the specified point. 89) Point T Q U - P R T (, 0) S Graph the function over a one-period interval. 90) = sin ( - ) Determine the equation of the function that is graphed. 9) Find the amplitude, period, or phase shift as specified. 9) Find the amplitude of = cos +. 8

9 9) Find the period of = sin +. 9) Find the phase shift of = 5 + sin +. Graph the function over a one-period interval. 95) = sin ( - ) + 5 9) = cos - 5-9

10 Determine the equation of the function that is graphed. 97) ) Solve the problem. 99) Let f() = cos, g() = - /, and h() =. Find f(g(/)). 00) The voltage E in an electrical circuit is given b E =.8 cos 50t, where t is time measured in seconds. Find the period. 0) The voltage E in an electrical circuit is given b E =. cos 0t, where t is time measured in seconds. Find the frequenc of the function (that is, find the number of ccles or periods completed in one second).. Find the eact value for the epression. 0) sec 0) csc Use a calculator to find the function value to four decimal places. 0) csc (.0) 0

11 Indicate the period and the range of the given function. 05) = sec + Graph the function. 0) = csc ) = 5 csc

12 08) = 5 sec Find the equation for the curve in its final position. 09) The graph of = cot () is shifted a distance of / to the right, stretched b a factor of, translated 7 units upward, then reflected in the -ais. Find the equations for all vertical asmptotes for the function. 0) = csc ( + ) ) = sec. Find the eact value for the epression. ) tan - ) cot Use a calculator to find the function value to four decimal places. ) cot (.) Determine the period of the function. 5) = cot

13 Graph the function. ) = tan ) = cot Find the equation for the curve in its final position. 8) The graph of = cot () is shifted a distance of / to the left, reflected in the -ais, then translated 7 units upward.

14 Answer Ke Testname: 00 CH AND REVIEW ) 5, -98 ) 8, -9 ),- ) II 5) I ) 88 7) 0 8) ) -7 7''' 0) 5' ) 9 7' " ) - ) 0.57 ) ) ) ) 5, ) I 9) II 0) II ) )

15 Answer Ke Testname: 00 CH AND REVIEW ) ) 7 5) - ) 0. m 7) in. 8) sq cm 9) 0 0 in. 0) 00 rad/min ) 9 radians/sec ) 58 ft/min ) in./min ) 5 5) ) ) - 8) - 9) 0) ) - ) ) ) ) 0.0 ) 7) 8) I 9) IV 5

16 Answer Ke Testname: 00 CH AND REVIEW 50) III 5) 5 5) 0 5) 5 5) -0 55) 5 5) 8. 57) 7. 58) 5 59) 5 0) 0 ) α =.9, b =., c =. ) a =., α =.8, b =.5 ) 8 ft ) 0 ft 5) ) ) 8) 7 9)

17 Answer Ke Testname: 00 CH AND REVIEW 70) 7) 7 7) 7) - 7) 75) 7) - 77) True 78) False 79) 8 ft 80) - 8) - 8) 8) - 8) - 85) 8) (0, -5) 87) (7/,-7) 88), 5 89), 0 7

18 Answer Ke Testname: 00 CH AND REVIEW 90) ) = cos 9) 9) 9) - 95) 5 9) 5-97) = sin (-) 98) = sin 8

19 Answer Ke Testname: 00 CH AND REVIEW 99) 00) 5 0) 80 0) - 0) - 0) ) P = ; Range: 0) ) )

20 Answer Ke Testname: 00 CH AND REVIEW 09) = - cot ) = k ) = + k ) ) - ) 0.9 5) ) - - 7) ) = -cot