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Pre-Calculus Assignment SheetUnit 3: Basic TrigonometrySeptember 24th – October 11th, Friday10/4Topic(4.1) Angles in Coordinate Plane – DegreesNotes pages 1 and 2Paper Plate Activity for the Unit CircleAssignmentp.291 #31 – 46 all30-60-90 and 45-45-90 right triangles place coordinateson the plate and go over HW from Mondayp. 299 #5 – 21 odd(4.1) Angles in Coordinate Plane – RadiansNotes page 3(4.4) Reference AnglesNotes page 4 QUIZ– Angles in Radians and Degrees(4.1) Arc Length and Sector Area Notes pages 4 & 5(4.3) Right Triangle TrigonometryNotes bottom of page 5(4.2) Unit Circle (day 3) discuss period and even/oddqualities of trig functions Notes top of page 6p. 290 #7 – 23, 47 – 54 all, 55 – 69 oddMonday10/7 QUIZ- Arc Length, Sector Area, Reference Angles(4.3) Evaluate Trig Functions with a Calculator usingBasic Trig Identities (introduce cofunctions p. 374)Notes bottom of page 6(4.4) Trig Functions of any Value determine trigfunctions of any angles (in terms of x, y, and r), signs oftrig values in quads /- Notes p.7 QUIZ– Unit Circle (fill in the blanks)4.4 more calculator trig , finding solutions to equationsusing unit circle Notes p.7More Practice/ reviewpp.365 – 366 #3-87 odd – omit #s 21, 53, 55p. 300 #43 – 52p. 309 #27 – 35, 43 – NotesComplete Paper Plate Unit CircleNO SCHOOLTEST #3Basic Trigonometry (4.1 – 4.4)September 24th, 2013p. 319 #37 – 44 (reference angles)p. 292 #79 – 94 ,#95 – 100, 106, 107p. 308 #1 – 4 all, 9 – 15 odd, 17 – 20 allp. 299 # 1, 3, 23 – 41 oddp. 318 #1 – 7 odd, 11 – 14 all,15 – 23 odd, 29 – 36 all, 45 – 64 allp. 319 #65 – 86Study for test tomorrow!!!Print Unit 4(4.1) Angles in Coordinate Plane – DegreesVocab:angle in standard positioninitial sideterminal sidevertexpositive anglesnegative anglescoterminal anglesrotationDraw and label degrees of circle on the axis of the coordinate plane.1
State the Quadrant in which the terminal side of the given angle lies and draw the angle in standard position.1. 187 2. – 14.3 3. 245 4. – 120 5. 800 6. 1075 7. – 460.5 8. 315 9. – 912 10.11. 537 12. – 345.14 13 Find two angles, one positive and one negative angle, that are coterminal with the given angle.13. 74 14. – 81 15. 115.3 16. 275 Find the complement and supplement for the given angles.17. – 180 19. 17.11 18. – 310 20. 45.2 Find the degree measure of the angle for each rotation. Draw the angle in standard position.21.5rotation, clockwise822.3rotation, counterclockwise523.7rotation, counterclockwise924.17rotation, clockwise425.3rotation, clockwise1026.5rotation, counterclockwise62
September 30th, 2013Notes(4.1) Angles in Coordinate Plane – RadiansDetermine the quadrant in which each angle lies and sketch the angle in standard position.1. 72. 93.6 54. 5 75.17 86.3.7 r7. 4.2 rFind the complement and supplement of each angle, if possible.8. 79.6 510.3r11.Find the Radian Measure of the angle with the given Degree Measure12. 330 13. –72 14. 145 15. 765 Find the Degree Measure of the angle with the given Radian Measure.18. 7 219.5 620.1.5 r2 921. 1216. 36 22. 2r17. –120 23. -1.5rIII. Find two co-terminal angles for the following. One Positive and One Negative.24. 135 25.11 626. 27. -50 4IV. Determine if the following are co-terminal.28. -30 , 330 29.5 17 ,6630.32 11 ,3331. 50 , 340 3
October 1st, 2013Notes:Reference AnglesDefinition of a reference angle:Find the reference angle1. 32 6. 11. 71.4 r 'and sketch2. 132 7. 12. 9 72.8 r ' in standard position.3. 132 8. 13.October 2nd, 2013Notes:and 4 54.22 r4. 232 9. 14. 2 75.95 r5. 200 20 910. 15. 1.7 rArc Length and Area of a SectorArc lengthArea of a SectorFind the length of the arc on a circle of radius, r, with central angle, .1.r 4; 62.r 3.5; 3 43.r 10; 60 Find the radian measure of the central angle of a circle with radius, r, that intercepts an arc length, s.4. r 20, s 155. r 33 inches, s 6 inchesFind the area of a sector with radius, r, and central angle, .4
1.r 5; 120 2.r 8.4; 2 3Applications1. Pittsburg, PA is located at 40.5 N while Miami is located at 25.5 N. Assuming the Earth is a perfect sphere, how many milesapart are the two cities (Earth radius is 4,000 miles).2. A sprinkler can spray water 75 feet and rotates through an angle of 135 . Find the area of the region that the sprinkler covers.October 3rd, 2013Notes:hypotenuseRight Triangle Trigonometrysideopposite side adjacent tosin csc cos sec tan cot Find the exact value of the six trigonometricfunctions of the angle shown in the figure.2. Sketch a right triangle corresponding to the trig function,determine the third side and then find the 5 remaining trig functions.csc 310 245
October 4th, 2013Notes:Even, odd qualities of Trig FunctionsGiven the coordinate, determine the exact value of the six trig functions.1. 5 12 , 13 13 2. 15 8 , 17 17 5.sinEvaluate the trig function using its period and your plate.3. cos 7 4.EVEN Trig. functions:ODD Trig functions:6. Ifsin11 4cos( x) cos xsin( x) sin xtan( x) tan xcsc t 5 then csc( t ) and6.cos 15 6sec( x) sec xcsc( x) csc xcot( x) cot xsin t then sin( t ) October 7th, 2013Notes: 7 2Cofunctions, Calculator Trig.Cofunction Identities: sin u cos u 2 cos u sin u 2 tan u cot u 2 csc u sec u 2 sec u csc u 2 Remember 2 cot u tan u 2 90 Use a calculator to evaluate the trig. function, Round to 4 decimal places.1.sin 55. cos 38 3 72.csc6.cot 77.5 3.tan1.287. sin 57.8 4.sec .778.csc 29.5 Use the given function values to find the indicated trig values. Draw a triangle or use your plate.9.10.cos 30 12tan 3tan 30 sec 30 cos(90 30 ) cot sin sin 90 6
October 8th, 2013Notes:Trig Functions of any angleDefinition of Trig Functions of any angle: Leta point on the terminal side ofsin and be an angle in standard position with ( x, y)r x 2 y 2 0 . Then:cos csc 1. Determine the exact value of the 6 trig functions givenState the quadrant(s) in whichsec cot tan (4, 7) . Draw a triangle. lies.2.tan 03.sin 0 tan 04.cos 05.sin 0 cos 06.sin cos 7.sin 0 cos 0Find the values of the 6 trig functions with the given restraints. Draw a triangle.8.cos Find10.359. csc 2 lies in Quadrant IV , for 0 , for the following problems.sin 32 11.October 9th, 2013Notes:1.cos 125 5.sec3 5cos 0Put answer in radians.cos 1 12.tan undefined More Calculator Trig and Solving Trig Equations2.csc168 3.cot 150 4.sin 345 6.cos 2 77.tan13 88.sin 3.42 rFind two solutions for the given equations. Use your paper plate.9.cos 3210.sin 3211.csc 212.cot 37
Notes September 30th, 2013 (4.1) Angles in Coordinate Plane - Radians Determine the quadrant in which each angle lies and sketch the angle in standard position. 1. 7 S 2. 9 S 3. 5 6S 4. 7 5S 5. 8 17S 6. 3.7r 7. 4.2r Find the complement and supplement of each angle, if possible. 8. 9. 10. 3r 11. 1.5r Find the Radian Measure of the angle with .
