( 6π ) Applications of Trig Functions

Transcription

1 8.8 - Applicatins f Trig Functins 1. The geese ppulatin in a certain area fluctuates peridically between a maximum f 600 geese and a minimum f 350 geese. This ppulatin cycle repeats every 5 years. Write a sine functin t the mdel the geese ppulatin when time is measured in years. 2. The average mnthly temperature in Greenville varies peridically with a maximum f 69 F and a minimum f 41 F. A cmplete cycle repeats every year. Write a csine functin t mdel the temperature in Greenville when time is measured in mnths. ( 6π ) The functin f (x) 33cs x 0 mdels the height f a rider n a Ferris wheel, where x represents time in minutes. Determine the maximum and minimum height the rider reaches, and determine the amunt f time it takes fr the rider t cmplete a full revlutin. 4. A Ferris wheel has a diameter f 92 m and makes a cmplete revlutin every 8 minutes.. The wheel starts turning when a rider is at its lwest pint, 9 m abve the grund. Write a csine functin t mdel the rider s height abve the grund when time is measured in minutes. 5. The functin f (x) 1.3cs (4πx) mdels the altitude f the midday sun at Venus s equatr, where x represents time in years. Determine the maximum and minimum altitude the sun reaches, and determine the amunt f time it takes fr the sun t cmplete a full cycle. 6. When an appliance is plugged int an utlet, vltage fluctuates between psitive and negative values. In Barbads, the vltage fluctuates between 163 vlts and 163 vlts with a frequency f 50 cycles per secnd. Write a sine functin t mdel the vltage when time is measured in secnds.

2 Name Math 3 Unit 8: Trignmetry May 7 May 8 May 9 May 10 May 11 Angles in degrees HW: wrksheet 8.1 Angles in radians HW: wrksheet 8.2 Right triangle trig HW: wrksheet 8.3 Unit circle Exact values f sine and csine HW: wrksheet 8.4 QUIZ!! Exact values f all trig functins HW: wrksheet 8.5 May 14 May 15 May 16 May 17 May 18 Graphs f sine and csine HW: wrksheet 8.6 Equatins f sine and csine HW: wrksheet 8.7 QUIZ!! Applicatins f trig functins HW: wrksheet 8.8 Review fr test HW: finish review TEST!!!

3 8.1 - Angles and Their Measures in Degrees Draw each angle in standard psitin Find ne psitive and ne negative cterminal angle that crrespnds t the given angle Determine an angle between 0 and 360 that is cterminal t the given angle

4 8.7 - Equatins f Sine and Csine Wrksheet 1. y 4 cs4x y 6sin x 4 3 Amplitude: Perid: Frequency: Vertical Shift: Amplitude: Perid: Frequency: Vertical Shift: 3. y s inx y 2 cs x 3 Amplitude: Perid: Frequency: Vertical Shift: Amplitude: Perid: Frequency: Vertical Shift: 5. y 2cs8x 4 6. y s in3x + 1 Amplitude: Perid: Frequency: Vertical Shift: Amplitude: Perid: Frequency: Vertical Shift: 7. Given an amplitude f 7, a perid f 4π, and a vertical shift dwn 3 units, write the equatin f the sine functin. 8. Given an amplitude f 3, a frequency f π 1, and a vertical shift up 7 units, write the equatin f the csine functin. 9. Given an amplitude f 7456, a perid f, and a vertical shift up units, write the equatin f the π 46 sine functin.

5 8.6 - Graphs f Sine and Csine Determine the amplitude, perid, frequency, vertical shift, and equatin fr each graph belw. A B C D Amplitude Perid Frequency Vertical Shift Equatin A B C D

6 8.2 - Angles and Their Measures in Radians Cnvert angle in degrees t radians Cnvert each angle in radians t degrees π 6. 3π 4 11π π Draw each angle in standard psitin. 9. 5π π π 7π π 13. π π π 6

7 8.3 - Right Triangle Trig Slve fr the variable The flagple casts a shadw 40 feet lng when the measurement f the angle f elevatin t the sun is 31. Hw tall is the flagple? 8. A submarine dives at an angle f depressin f 15. It travels a hrizntal distance f 1500 feet during the dive. What is the depth f the submarine after the dive? 9. Sally is standing a distance away frm a skyscraper that is 780 feet tall. Marcie is between Sally and the skyscraper. The angle f elevatin frm Sally s psitin t the tp f the skyscraper is 42. The angle f elevatin frm Marcie s psitin t the tp f the skyscraper is 71. Hw far is Sally frm Marcie?

8 Use the unit circle t determine the exact value f each trignmetric functin. 1. sin cs tan60 4. sin π 6 5. sec 2π 3 6. ct 5π 3 7. tan90 8. c sπ 9. csc 3π s in2π 11. cs sec ct sin π cs sec 7π 6

9 8.5 - Exact Values f Trig Functins Cmplete the unit circle

10 .said n teacher ever. Turn the page t get t hmewrk 8.4 (Like I wuld really give yu a day withut hmewrk. Puh-lease)

11 8.4 - Exact Values f Sine and Csine wrksheet Cmplete the unit circle.

12 Use the unit circle t determine the exact value f each trignmetric functin. 1. sin c s 0 3. sin cs 3π 4 5. sin 4π 3 6. cs sin 8π 3 8. cs sin cs sin 270 π 12. cs 3 11π 13. sin 3π 14. cs 6