Mathematics 30-1: Unit 2 2 Lesson A - Assignment Booklet 1. If the point (x, - 5 ) is a point on the unit circle in Quadrant IV, then the 9 exact value of x is - 2 14 A. 9 2 14 B. 9 - 106 C. 9 106 D. 9 2 2. The point which is not on the unit circle is 1 2 1 2 ,\tA. c m B. (- 2 , - 2 ) c- 2 , 2 m C 2 2 D. e, 1 o 2 2 2 Lesson A - Assignment Booklet 2 Mathematics 30-1: Unit 2 3 1 3. The angle i which makes the function P ( i ) = c 2 , - 2 m true, could be A. 7r 6 r B. 3 r 3 C. D. - 7r 6 Numeric Response 1 2 2 If the point (-0.58, y) is a point on the unit circle and 0 < y < 1 then the value of y, to the nearest hundredth is 4. An angle co-terminal with 5r is 7 A. - 9r 7 2r B. 7 12r C. 7 20r D. 7 2 5. Convert the rotational angle measure of 1 radian to degrees. Select the correct degree measure rounded to one decimal place A.\t180.0 B. 57.3 C. 3.1 D.\t0.3 Mathematics 30-1: Unit 2 2 Lesson A - Assignment Booklet 19r 6. Select the correct quadrant that the terminal arm of 6 lies in and also the principal angle co-terminal to it. A. Quadrant II, r 6 B. Quadrant III, r 6 7r C. Quadrant II, 6 7r D. Quadrant III, 6 Numeric Response 2 2 A circle has a radius of 5 cm. A central angle measures 333. Determine the arc length subtended by the two radii making the central angle rounded to two decimal places. 2 7. A flywheel makes one full rotation every 20 seconds. What is the full angle of rotation after 3 minutes? A. 18r radians B. 0r radians 2r radians C. D. 9r radians Lesson A - Assignment Booklet Mathematics 30-1: Unit 2 Written Response 4 2 Draw the angle i = Determine the negative rotation angle which is co-terminal to this angle. Determine the coordinates of the point on the unit circle where the terminal arm of intersects the unit circle. 2. What is the central angle of a circle when the arc length and the radius are equal? Describe a situation when this might occur. Total: 7r in standard position on a unit circle. 4 1. 24 Mathematics 30-1: Unit 2 Lesson A - Assignment Booklet Mathematics 30-1: Unit 2 2 Lesson B - Assignment Booklet 3 1. The exact value of sec 4p is 3 -2 A. 3 B.\t-2 C. 2 3 3 2 D. 1 2. If sin = 0.4321 and 90 < < 360, then , to the nearest degree, is A. 116 B. 26 C. 154 D. 206 Numeric Response 1 1 If the terminal arm of angle intersects the unit circle at the point c - 3 , - 55 m , then, 8 8 to the nearest hundredth of a radian, is Lesson B - Assignment Booklet 2 Mathematics 30-1: Unit 2 3. The solutions to the trig equation 4cos + 3 = 0 are in which Quadrants? A. 3 and 4 B. 1 and 2 C. 1 and 4 D. 2 and 3 2 4. The general solution to the equation 2tan = 2 is 4 = + n , n I A. 3 4 = + n , n I B. 4 = + 2n, n I C. 3 4 = + 2n, n I D. 3 5. The solution to 2sin2 = 1, 0 < < 360, is A. 45, 135, 225, 315 B. 45, 135 C. 30, 150 D. 30, 150, 210, 330 Mathematics 30-1: Unit 2 Lesson B - Assignment Booklet Written Response 4 4 2 3 and -270 < < 180, 3 1. Given csc i = Determine the exact values of . Determine the coordinates of the points on the unit circle where the terminal arm of intersect the unit circle. Determine the exact values of cos and tan . 2. Given the equation 6cossin - 2cos = 0, Solve this equation, to the nearest tenth of a degree, in the domain, 0 < < 360. Determine the general solution to the equation. Total: 19 1. If the point (x,-5/9) is a point on the unit circle in Quadrant IV, then the exact value of x is. 2. The point which is not on the unit circle is The points in the unit circle have to be less than 1 unit, for boyh the x and y axis. All the oints satisfy that except (2 , 2 ) 3. The angle i which makes the function tan = P()= ( 12 , 23 ) true, could be y x 3 2 tan = 1 2 tan = 3=1.732 =atan 1.732 =60 o o equivalent of 60 radians 602 360 3 Numeric Response 1 If the point (-0.58, y) is a point on the unit circle and 0 < y < 1 then the value of y, to the nearest hundredth is x + y =1 so ,(0.58)+ y =1 2 y =1 (0.58 ) 2 2 y =0.6636 since y <1 y=0.81 4. An angle co-terminal with 2 5 7 5 7 is y= 0.81 9 7 5. Convert the rotational angle measure of 1 radian to degrees. Select the correct degree measure rounded to one decimal place 2 rad=360 o 1rad =? 360 o 2 57.3 o 6. Select the correct quadrant that the terminal arm of 19 6 lies in and also the principal angle co-terminal to it. 19 7 =2 + 6 6 Numeric Response 2 A circle has a radius of 5 cm. A central angle measures 333. Determine the arc length subtended by the two radii making the central angle rounded to two decimal places. r=5 cm o =333 convert deg . rad 3302 =5.7596 rad 360 arc length=r 55.7596 28.80 cm 7. A flywheel makes one full rotation every 20 seconds. What is the full angle of rotation after 3 minutes? Written response 1. Draw the angle = 7 4 in standard position on a unit circle. = 7 4 2 =360o 7 =? 4 7 360o 4 =315o 2 drawing 315 o Determine the negative rotation angle which is co-terminal to this angle. radians 2 7 4 1 4 degrees o angle=360 315 o 45o 2. What is the central angle of a circle when the arc length and the radius are equal? Describe a situation when this might occur. This occurs when the angle at the center of a unit circle is equal to 1 radian. 1. The exact value of sec sec ( 43 ) ( 43 )=2 2. If sin = 0.4321 and 90 < < 360, then , to the nearest degree, is sin =0.4321 =arcsin(0.4321) =25.6 but issecond quadrant =90 +25.6 115.6 116 Numeric Response 1 Terminal point = (3/8, 55/8) 55 y 8 55 tan = = = x 3 3 8 isquadrant III Since x <0 y< 0 =arctan ( 355 )+ 4.3279 3. The solutions to the trig equation 4cos + 3 = 0 are in which Quadrants? 4 cos +3=0 cos =3 /4 ( 34 ) 3 =arccos ( ) 4 =arccos 41.4 but cosine is negativequadrant II =18041.4 138.6 deg . quadrant III =180+ 41.4 121.4 deg . 4. The general solution to the equation 2tan = 2 is From the equation 2 tan = =1 2 =arctan 1=45 deg . rad .= pi 4 General f ormula Since period for tan = pi General formula = 5. pi +npi 4 The solution to 2sin2 = 1, 0 < < 360, is si n2 = 1 2 sin = 1 2 2 sin = 2 2 2 sin = sin = 2 2 Solving for =arcsin sin = 2n 2 ( 22 ) =45 deg . anglesquadrnant I II sin = Solving for =arcsin 2 n 2 ( 22 ) =45 deg . anglesquadrant III IV =45 , 135,225, 315 Written Response 1. Given csc = 2 3 3 and -270 < < 180 Exact values of 1 2 3 =csc = sin 3 sin = 3 2 3 =arcsin ( 2 3 3 ) o =60 since sine is positive isquadrant I II o =60 2. Given the equation 6cossin - 2cos = 0, Solve this equation, to the nearest tenth of a degree, in the domain, 0 < < 360. 6 cos sin2 cos=0 2 cos(3 sin1)=0 =arccos0 =90 since cos is positive it i squadrant I IV =90 , 270 3 sin - 1=0 3 sin =1 cos =0 sin = 1 3 =arcsin ( 13 ) =19.5 since sin is positive , isquadrant I II =19.5 , 160.5 Determine the general solution to the equation. =90+360 k =270+ 360 k =180sin (1 /3)+360 k =sin (1/3)+360 k 1. If the point (x,-5/9) is a point on the unit circle in Quadrant IV, then the exact value of x is. 2. The point which is not on the unit circle is The points in the unit circle have to be less than 1 unit, for boyh the x and y axis. All the oints satisfy that except (2, 2) 1 3. The angle i which makes the function () = (2 , 3 ) true, 2 could be tan = 3 2 tan = 1 2 tan = 3 = 1.732 = atan 1.732 = 60 60 60 2 = 360 = 3 Numeric Response 1 If the point (-0.58, y) is a point on the unit circle and 0 < y < 1 then the value of y, to the nearest hundredth is + = 1 , (0.58) + = 1 2 = 1 (0.58)2 2 = 0.6636 = 0.81 < 1 = 0.81 4. An angle co-terminal with 5 7 is 5 7 9 = 7 = 2 5. Convert the rotational angle measure of 1 radian to degrees. Select the correct degree measure rounded to one decimal place 2 = 360 1 =? 360 = 2 = 57.3 6. Select the correct quadrant that the terminal arm of 19 6 lies in and also the principal angle co- terminal to it. 19 7 = 2 + 6 6 Numeric Response 2 A circle has a radius of 5 cm. A central angle measures 333. Determine the arc length subtended by the two radii making the central angle rounded to two decimal places. = 5 = 333 . 330 2 = = 5.7596 360 = = 5 5.7596 = 28.80 7. A flywheel makes one full rotation every 20 seconds. What is the full angle of rotation after 3 minutes? Written response 1. Draw the angle = 7 4 in standard position on a unit circle. 7 = 4 2 = 360 7 =? 4 7 4 360 = 315 2 315 Determine the negative rotation angle which is co-terminal to this angle. 7 = 2 4 1 = 4 = 360 315 = 45 2. What is the central angle of a circle when the arc length and the radius are equal? Describe a situation when this might occur. This occurs when the angle at the center of a unit circle is equal to 1 radian. 4 1. The exact value of sec ( 3 ) 4 sec ( ) = 2 3 2. If sin = 0.4321 and 90 < < 360, then , to the nearest degree, is = 0.4321 = (0.4321) = 25.6 = 90 + 25.6 = 115.6 = 116 Numeric Response 1 Terminal point = (3/8, 55/8) 55 8 55 = = = 3 3 8 < 0 < 0 55 = ( )+ 3 = 4.3279 3. The solutions to the trig equation 4cos + 3 = 0 are in which Quadrants? 4 + 3 = 0 = 3/4 3 = ( ) 4 3 = ( ) 4 = 41.4 = 180 41.4 = 138.6 . = 180 + 41.4 = 121.4 . 4. The general solution to the equation 2tan = 2 is From the equation 2 =1 2 = 1 = 45 . = 4 = = + 4 . = 5. The solution to 2sin2 = 1, 0 < < 360, is 2 = 1 2 1 = 2 sin = sin = Solving for sin = 2 2 2 2 sin = 2 2 2 2 2 ) 2 = 45 . = arcsin ( Solving for sin = 2 2 2 ) 2 = 45 . = 45, 135, 225, 315 = arcsin ( Written Response 1. Given = 23 3 and -270 < < 180 Exact values of 1 23 = = sin 3 3 sin = 23 3 = arcsin ( ) 23 = 60o sine is positive is in quadrant I or II = 60o 2. Given the equation 6cossin - 2cos = 0, Solve this equation, to the nearest tenth of a degree, in the domain, 0 < < 360. 6 2 = 0 2 (3 1) = 0 = 0 = 0 = 90 = 90, 270 3 - 1 = 0 3 = 1 1 = 3 1 = ( ) 3 = 19.5 , = 19.5, 160.5 Determine the general solution to the equation. = 90 + 360 = 270 + 360 = (1/3) + 360 = 180 (1/3) + 360 1. If the point (x,-5/9) is a point on the unit circle in Quadrant IV, then the exact value of x is. , 2 + 2 = 2 = 1 2 + 2 = 12 5 2 2 + ( ) = 1 9 5 2 2 = 1 ( ) 9 25 2 = 1 81 56 2 = 81 56 = 81 = 0.8315 , = 0.8315 2. The point which is not on the unit circle is The points in the unit circle have to be less than 1 unit, for boyh the x and y axis. All the oints satisfy that except (2, 2) 1 2 3. The angle i which makes the function () = ( , 3 ) true, 2 could be tan = 3 2 tan = 1 2 tan = 3 = 1.732 = atan 1.732 = 60 60 60 2 = 360 = 3 Numeric Response 1 If the point (-0.58, y) is a point on the unit circle and 0 < y < 1 then the value of y, to the nearest hundredth is + = 1 , (0.58) + = 1 2 = 1 (0.58)2 2 = 0.6636 = 0.81 < 1 = 0.81 4. An angle co-terminal with 5 7 is 5 7 9 = 7 = 2 5. Convert the rotational angle measure of 1 radian to degrees. Select the correct degree measure rounded to one decimal place 2 = 360 1 =? 360 = 2 = 57.3 6. Select the correct quadrant that the terminal arm of 19 6 lies in and also the principal angle co- terminal to it. 19 7 = 2 + 6 6 Numeric Response 2 A circle has a radius of 5 cm. A central angle measures 333. Determine the arc length subtended by the two radii making the central angle rounded to two decimal places. = 5 = 333 . 330 2 = = 5.7596 360 = = 5 5.7596 = 28.80 7. A flywheel makes one full rotation every 20 seconds. What is the full angle of rotation after 3 minutes? Written response 1. Draw the angle = 7 4 in standard position on a unit circle. 7 = 4 2 = 360 7 =? 4 7 4 360 = 315 2 315 Determine the negative rotation angle which is co-terminal to this angle. 7 = 2 4 1 = 4 = 360 315 = 45 2. What is the central angle of a circle when the arc length and the radius are equal? Describe a situation when this might occur. This occurs when the angle at the center of a unit circle is equal to 1 radian. 1. If the point (x,-5/9) is a point on the unit circle in Quadrant IV, then the exact value of x is. , 2 + 2 = 2 = 1 2 + 2 = 12 5 2 2 + ( ) = 1 9 5 2 2 = 1 ( ) 9 25 2 = 1 81 56 2 = 81 56 = 81 = 0.8315 , = 0.8315 2. The point which is not on the unit circle is The points in the unit circle have to be less than 1 unit, for boyh the x and y axis. All the oints satisfy that except (2, 2) 1 2 3. The angle i which makes the function () = ( , 3 ) true, 2 could be tan = 3 2 tan = 1 2 tan = 3 = 1.732 = atan 1.732 = 60 60 60 2 = 360 = 3 Numeric Response 1 If the point (-0.58, y) is a point on the unit circle and 0 < y < 1 then the value of y, to the nearest hundredth is + = 1 , (0.58) + = 1 2 = 1 (0.58)2 2 = 0.6636 = 0.81 < 1 = 0.81 4. An angle co-terminal with 5 7 is 5 7 9 = 7 = 2 5. Convert the rotational angle measure of 1 radian to degrees. Select the correct degree measure rounded to one decimal place 2 = 360 1 =? 360 = 2 = 57.3 6. Select the correct quadrant that the terminal arm of 19 6 lies in and also the principal angle co- terminal to it. 19 7 = 2 + 6 6 Numeric Response 2 A circle has a radius of 5 cm. A central angle measures 333. Determine the arc length subtended by the two radii making the central angle rounded to two decimal places. = 5 = 333 . 330 2 = = 5.7596 360 = = 5 5.7596 = 28.80 7. A flywheel makes one full rotation every 20 seconds. What is the full angle of rotation after 3 minutes? 20 = 360 (3 60) =? 3 60 360 = 20 = 3240 Written response 1. Draw the angle = 7 4 in standard position on a unit circle. 7 4 2 = 360 7 =? 4 7 4 360 = 315 2 315 = Determine the negative rotation angle which is co-terminal to this angle. 7 = 2 4 1 = 4 = 360 315 = 45 2. What is the central angle of a circle when the arc length and the radius are equal? Describe a situation when this might occur. This occurs when the angle at the center of a unit circle is equal to 1 radian. 1. If the point (x,-5/9) is a point on the unit circle in Quadrant IV, then the exact value of x is. 2. The point which is not on the unit circle is The points in the unit circle have to be less than 1 unit, for boyh the x and y axis. All the oints satisfy that except (2 , 2 ) 3. The angle i which makes the function tan = P()= ( 12 , 23 ) true, could be y x 3 2 tan = 1 2 tan = 3=1.732 =atan 1.732 =60 o o equivalent of 60 radians 602 360 3 Numeric Response 1 If the point (-0.58, y) is a point on the unit circle and 0 < y < 1 then the value of y, to the nearest hundredth is x + y =1 so ,(0.58)+ y =1 2 y =1 (0.58 ) 2 2 y =0.6636 since y <1 y=0.81 4. An angle co-terminal with 2 5 7 5 7 is y= 0.81 9 7 5. Convert the rotational angle measure of 1 radian to degrees. Select the correct degree measure rounded to one decimal place 2 rad=360 o 1rad =? 360 o 2 57.3 o 6. Select the correct quadrant that the terminal arm of 19 6 lies in and also the principal angle co-terminal to it. 19 7 =2 + 6 6 Numeric Response 2 A circle has a radius of 5 cm. A central angle measures 333. Determine the arc length subtended by the two radii making the central angle rounded to two decimal places. r=5 cm o =333 convert deg . rad 3302 =5.7596 rad 360 arc length=r 55.7596 28.80 cm 7. A flywheel makes one full rotation every 20 seconds. What is the full angle of rotation after 3 minutes? Written response 1. Draw the angle = 7 4 in standard position on a unit circle. = 7 4 2 =360o 7 =? 4 7 360o 4 =315o 2 drawing 315 o Determine the negative rotation angle which is co-terminal to this angle. radians 2 7 4 1 4 degrees o angle=360 315 o 45o 2. What is the central angle of a circle when the arc length and the radius are equal? Describe a situation when this might occur. This occurs when the angle at the center of a unit circle is equal to 1 radian. 1. The exact value of sec sec ( 43 ) ( 43 )=2 2. If sin = 0.4321 and 90 < < 360, then , to the nearest degree, is sin =0.4321 =arcsin(0.4321) =25.6 but issecond quadrant =90 +25.6 115.6 116 Numeric Response 1 Terminal point = (3/8, 55/8) 55 y 8 55 tan = = = x 3 3 8 isquadrant III Since x <0 y< 0 =arctan ( 355 )+ 4.3279 3. The solutions to the trig equation 4cos + 3 = 0 are in which Quadrants? 4 cos +3=0 cos =3 /4 ( 34 ) 3 =arccos ( ) 4 =arccos 41.4 but cosine is negativequadrant II =18041.4 138.6 deg . quadrant III =180+ 41.4 121.4 deg . 4. The general solution to the equation 2tan = 2 is From the equation 2 tan = =1 2 =arctan 1=45 deg . rad .= pi 4 General f ormula Since period for tan = pi General formula = 5. pi +npi 4 The solution to 2sin2 = 1, 0 < < 360, is si n2 = 1 2 sin = 1 2 2 sin = 2 2 2 sin = sin = 2 2 Solving for =arcsin sin = 2n 2 ( 22 ) =45 deg . anglesquadrnant I II sin = Solving for =arcsin 2 n 2 ( 22 ) =45 deg . anglesquadrant III IV =45 , 135,225, 315 Written Response 1. Given csc = 2 3 3 and -270 < < 180 Exact values of 1 2 3 =csc = sin 3 sin = 3 2 3 =arcsin ( 2 3 3 ) o =60 since sine is positive isquadrant I II o =60 2. Given the equation 6cossin - 2cos = 0, Solve this equation, to the nearest tenth of a degree, in the domain, 0 < < 360. 6 cos sin2 cos=0 2 cos(3 sin1)=0 =arccos0 =90 since cos is positive it i squadrant I IV =90 , 270 3 sin - 1=0 3 sin =1 cos =0 sin = 1 3 =arcsin ( 13 ) =19.5 since sin is positive , isquadrant I II =19.5 , 160.5 Determine the general solution to the equation. =90+360 k =270+ 360 k =180sin (1 /3)+360 k =sin (1/3)+360 k 1. If the point (x,-5/9) is a point on the unit circle in Quadrant IV, then the exact value of x is. 2. The point which is not on the unit circle is The points in the unit circle have to be less than 1 unit, for boyh the x and y axis. All the oints satisfy that except (2, 2) 1 3. The angle i which makes the function () = (2 , 3 ) true, 2 could be tan = 3 2 tan = 1 2 tan = 3 = 1.732 = atan 1.732 = 60 60 60 2 = 360 = 3 Numeric Response 1 If the point (-0.58, y) is a point on the unit circle and 0 < y < 1 then the value of y, to the nearest hundredth is + = 1 , (0.58) + = 1 2 = 1 (0.58)2 2 = 0.6636 = 0.81 < 1 = 0.81 4. An angle co-terminal with 5 7 is 5 7 9 = 7 = 2 5. Convert the rotational angle measure of 1 radian to degrees. Select the correct degree measure rounded to one decimal place 2 = 360 1 =? 360 = 2 = 57.3 6. Select the correct quadrant that the terminal arm of 19 6 lies in and also the principal angle co- terminal to it. 19 7 = 2 + 6 6 Numeric Response 2 A circle has a radius of 5 cm. A central angle measures 333. Determine the arc length subtended by the two radii making the central angle rounded to two decimal places. = 5 = 333 . 330 2 = = 5.7596 360 = = 5 5.7596 = 28.80 7. A flywheel makes one full rotation every 20 seconds. What is the full angle of rotation after 3 minutes? Written response 1. Draw the angle = 7 4 in standard position on a unit circle. 7 = 4 2 = 360 7 =? 4 7 4 360 = 315 2 315 Determine the negative rotation angle which is co-terminal to this angle. 7 = 2 4 1 = 4 = 360 315 = 45 2. What is the central angle of a circle when the arc length and the radius are equal? Describe a situation when this might occur. This occurs when the angle at the center of a unit circle is equal to 1 radian. 4 1. The exact value of sec ( 3 ) 4 sec ( ) = 2 3 2. If sin = 0.4321 and 90 < < 360, then , to the nearest degree, is = 0.4321 = (0.4321) = 25.6 = 90 + 25.6 = 115.6 = 116 Numeric Response 1 Terminal point = (3/8, 55/8) 55 8 55 = = = 3 3 8 < 0 < 0 55 = ( )+ 3 = 4.3279 3. The solutions to the trig equation 4cos + 3 = 0 are in which Quadrants? 4 + 3 = 0 = 3/4 3 = ( ) 4 3 = ( ) 4 = 41.4 = 180 41.4 = 138.6 . = 180 + 41.4 = 121.4 . 4. The general solution to the equation 2tan = 2 is From the equation 2 =1 2 = 1 = 45 . = 4 = = + 4 . = 5. The solution to 2sin2 = 1, 0 < < 360, is 2 = 1 2 1 = 2 sin = sin = Solving for sin = 2 2 2 2 sin = 2 2 2 2 2 ) 2 = 45 . = arcsin ( Solving for sin = 2 2 2 ) 2 = 45 . = 45, 135, 225, 315 = arcsin ( Written Response 1. Given = 23 3 and -270 < < 180 Exact values of 1 23 = = sin 3 3 sin = 23 3 = arcsin ( ) 23 = 60o sine is positive is in quadrant I or II = 60o 2. Given the equation 6cossin - 2cos = 0, Solve this equation, to the nearest tenth of a degree, in the domain, 0 < < 360. 6 2 = 0 2 (3 1) = 0 = 0 = 0 = 90 = 90, 270 3 - 1 = 0 3 = 1 1 = 3 1 = ( ) 3 = 19.5 , = 19.5, 160.5 Determine the general solution to the equation. = 90 + 360 = 270 + 360 = (1/3) + 360 = 180 (1/3) + 360 1. If the point (x,-5/9) is a point on the unit circle in Quadrant IV, then the exact value of x is. , 2 + 2 = 2 = 1 2 + 2 = 12 5 2 2 + ( ) = 1 9 5 2 2 = 1 ( ) 9 25 2 = 1 81 56 2 = 81 56 = 81 = 0.8315 , = 0.8315 2. The point which is not on the unit circle is The points in the unit circle have to be less than 1 unit, for boyh the x and y axis. All the oints satisfy that except (2, 2) 1 2 3. The angle i which makes the function () = ( , 3 ) true, 2 could be tan = 3 2 tan = 1 2 tan = 3 = 1.732 = atan 1.732 = 60 60 60 2 = 360 = 3 Numeric Response 1 If the point (-0.58, y) is a point on the unit circle and 0 < y < 1 then the value of y, to the nearest hundredth is + = 1 , (0.58) + = 1 2 = 1 (0.58)2 2 = 0.6636 = 0.81 < 1 = 0.81 4. An angle co-terminal with 5 7 is 5 7 9 = 7 = 2 5. Convert the rotational angle measure of 1 radian to degrees. Select the correct degree measure rounded to one decimal place 2 = 360 1 =? 360 = 2 = 57.3 6. Select the correct quadrant that the terminal arm of 19 6 lies in and also the principal angle co- terminal to it. 19 7 = 2 + 6 6 Numeric Response 2 A circle has a radius of 5 cm. A central angle measures 333. Determine the arc length subtended by the two radii making the central angle rounded to two decimal places. = 5 = 333 . 330 2 = = 5.7596 360 = = 5 5.7596 = 28.80 7. A flywheel makes one full rotation every 20 seconds. What is the full angle of rotation after 3 minutes? Written response 1. Draw the angle = 7 4 in standard position on a unit circle. 7 = 4 2 = 360 7 =? 4 7 4 360 = 315 2 315 Determine the negative rotation angle which is co-terminal to this angle. 7 = 2 4 1 = 4 = 360 315 = 45 2. What is the central angle of a circle when the arc length and the radius are equal? Describe a situation when this might occur. This occurs when the angle at the center of a unit circle is equal to 1 radian. 1. If the point (x,-5/9) is a point on the unit circle in Quadrant IV, then the exact value of x is. , 2 + 2 = 2 = 1 2 + 2 = 12 5 2 2 + ( ) = 1 9 5 2 2 = 1 ( ) 9 25 2 = 1 81 56 2 = 81 56 = 81 = 0.8315 , = 0.8315 2. The point which is not on the unit circle is The points in the unit circle have to be less than 1 unit, for boyh the x and y axis. All the oints satisfy that except (2, 2) 1 2 3. The angle i which makes the function () = ( , 3 ) true, 2 could be tan = 3 2 tan = 1 2 tan = 3 = 1.732 = atan 1.732 = 60 60 60 2 = 360 = 3 Numeric Response 1 If the point (-0.58, y) is a point on the unit circle and 0 < y < 1 then the value of y, to the nearest hundredth is + = 1 , (0.58) + = 1 2 = 1 (0.58)2 2 = 0.6636 = 0.81 < 1 = 0.81 4. An angle co-terminal with 5 7 is 5 7 9 = 7 = 2 5. Convert the rotational angle measure of 1 radian to degrees. Select the correct degree measure rounded to one decimal place 2 = 360 1 =? 360 = 2 = 57.3 6. Select the correct quadrant that the terminal arm of 19 6 lies in and also the principal angle co- terminal to it. 19 7 = 2 + 6 6 Numeric Response 2 A circle has a radius of 5 cm. A central angle measures 333. Determine the arc length subtended by the two radii making the central angle rounded to two decimal places. = 5 = 333 . 330 2 = = 5.7596 360 = = 5 5.7596 = 28.80 7. A flywheel makes one full rotation every 20 seconds. What is the full angle of rotation after 3 minutes? 20 = 360 (3 60) =? 3 60 360 = 20 = 3240 Written response 1. Draw the angle = 7 4 in standard position on a unit circle. 7 4 2 = 360 7 =? 4 7 4 360 = 315 2 315 = Determine the negative rotation angle which is co-terminal to this angle. 7 = 2 4 1 = 4 = 360 315 = 45 2. What is the central angle of a circle when the arc length and the radius are equal? Describe a situation when this might occur. This occurs when the angle at the center of a unit circle is equal to 1 radian