Mathacle PSet ---- Algebra, Trigonometry Functions Level Number Name: Date:

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1 PSet ---- Algebra, Trignmetry Functins I. DEFINITIONS OF THE SIX TRIG FUNCTIONS. Find the value f the trig functin indicated 1

2 PSet ---- Algebra, Trignmetry Functins Find the value f each trig functin. Rund the answers t the nearest tenthusandth 1.) cs ) tan 0 1.) sin 0 0.) csc 9 17.) csc 1 1.) csc 18.) cs 0.) ct

3 PSet ---- Algebra, Trignmetry Functins Answers 1.) 17/1.) 1/1.) /.) 17/1.).) 7.) / 8.) 11 9.) / 11.) / 1.) 1/ 1.) 7/ 1.) /7 1.) ) ) ) ) ) ) 1.) 1.0.) 0.

4 PSet ---- Algebra, Trignmetry Functins Find the measure f the angle indicated. Rund the answers t the nearest tenth.

5 PSet ---- Algebra, Trignmetry Functins Find the measure f the side indicated. Rund the answers t the nearest tenth.

6 PSet ---- Algebra, Trignmetry Functins Find the each triangle. Rund the answers t the nearest tenth.

7 PSet ---- Algebra, Trignmetry Functins Answers: 1.)..) 17.1.) 8..) 0.) 8.8.).9 7.). 8.) 9.) ) ) 1.). 1.). 1.) ). 1.) 17.) BC=1 mi, AB=. mi and A 8 18.) AC=7. in, AB=11. in, and B 9 19.) AB=.7 mi, BC= mi, and A 8 0.) AC= m, BC= m, and A 7 1.) AB=. mi, BC=1.mi, and B.) AC=1.8 mi, BC=.7 mi and B.) AC=. cm, BC=1.9 cm and B 0.) AB=.8 in, AC=. in and A 7

8 PSet ---- Algebra, Trignmetry Functins II. BASIC TRIG APPLICATIONS Find the values. Calculatr sectin. 1) Frm the tp f an il rig, m abve sea level, the angle f depressin f a ship is 1. Find the distance f the ship frm the base f the il rig, t the nearest meter..) The angle f depressin frm a helicpter t a speeding car is. If the helicpter is flying 00 m abve the grund, hw far is it frm the car?.) A tightrpe waler is abut t crss a rpe frm a dc t the bridge f a bat that is 1. m abve the level f the dc. The rpe is 1 m lng. At what angle f the inclinatin will the tightrpe waler be climbing?.) A persn is standing halfway between tw trees that are m apart. The angles f elevatin t the tps f the trees are and. Hw much taller is the ne tree ver the ther?.) Calculate the angle f elevatin f the line f sight f a persn whse eye is 1.7 m abve the grund, and is ling at the tp f a tree which is 7. m away n level grund and 18. m high. 8

9 PSet ---- Algebra, Trignmetry Functins.) While driving thrugh the muntains yu ntice a sign that shws a hill with an 11% grade. What angle des the rad mae with the hrizntal? 7.) A bat is tied t a pier by a -ft rpe. The pier is 1 feet abve the water. T the nearest degree, find the angle f depressin f the bat. 8.) Frm a pint away frm the base f a building, the angle f elevatin is 1. Frm a pint m clser t the building, the angle f elevatin increases t 7. Hw tall is the building? 9.) An bserver n a cliff, 10 meters abve sea level sights tw ships due east. The angles f depressin f the ships are 8 and. Find, t the nearest meter, the distance between the ships. 10.) A pilt flying at an altitude f 1,000 ft sights tw airprts directly in frnt f him. The angle f depressin t ne airprt is 78, and the angle f depressin t the secnd airprt is 19. What is the distance between the tw airprts? Rund t the nearest ft. 9

10 PSet ---- Algebra, Trignmetry Functins Answers 1.) 1 m.) 7 m.).7.) 0. m.) 1.7.). 7.).87 8.) 10. m 9.) 8 m 10.),00 ft 10

11 PSet ---- Algebra, Trignmetry Functins III. DEFINITIONS OF ANGLE MEASURE AND REFERENCE ANGLE Cnvert frm degrees t radians. Determine the quadrant f the terminals. 1.) 0 8.).) 90 9.) 1.) ) 0.) ) 1.) 11 1.) 101.) 8 1.) 10 7.) 70 1.) 180 Cnvert frm radians t degrees. Determine the quadrant f the terminals. 1.) 1.) ) 0 0.) ) 1.) 7 18.).) 11

12 PSet ---- Algebra, Basic Trignmetry Functins Find the reference angles..) 0.) 10.) 90.) 180.) 7.) 11.) 10 7.) 0 8.) ). 8.) 8 0.) 9.) 70 0.) 1.) 0 1.) 1.) 17.) 0.).) 71.) 101.) 1 1

13 PSet ---- Algebra, Basic Trignmetry Functins Answers 1), I.), y axis 1.), I 0.), II 8 ), II.), I 1 7.), y axis 7 8.), IV 7 9.), IV ), I 8 11.), I 0 1.), IV 7 1.), III 1 1.), x axis 1.) 0, I 1.) 18, I 17.) 11.9, II 18.) 108, III 19.) 00, III 0.) 1, II 1.) 1, II.) 100, IV.).).).) 7.) 8.) 9.) ) 1.).).).).).) ) 8.) 10 9.) 0. 0.) ).).).) 1

14 PSet ---- Algebra, Basic Trignmetry Functins V. EVALUATE THE TRIG FUNCTIONS. Assume that is an acute angle in a right triangle satisfying the given cnditins. Evaluate the remaining trignmetric functins. 1.) sin 7.) cs 11.) tan 9.) 11 ct.) csc 9.) 17 sec 1

15 PSet ---- Algebra, Basic Trignmetry Functins Evaluate the trignmetric functins. N Calculatr. 7.) Find sin and tan if cs and ct ) Find cs and ct ifsin and tan 0 9.) Find tan and sec ifsin and cs 0 10.) Find sin and cs if ct and sec ) Find sec and csc if ct and cs 0 1.) Find csc and ct if tan and sin 0 1

16 PSet ---- Algebra, Basic Trignmetry Functins Pint P is n the terminal side f angle. Evaluate the six trignmetric functins. 1.) 1.) 1.) 1.) 1

17 PSet ---- Algebra, Basic Trignmetry Functins Answers 1.) sin, 7 10 cs, 7 10 tan, 0 7 csc, 7 10 sec, 0 ct 10.) sin, 11 cs, 11 tan, 11 csc, 11 sec, ct.) 10 sin, cs, 10 tan, 9 10 csc, 10 sec, 9 ct 9.) sin, cs, tan, csc, 10 sec, ct ) 9 sin, 8 7 cs, 9 7 tan, csc, 9 7 sec, ct ) sin, 17 cs, tan, csc, 1 17 sec, ct 1 7.) sin, tan, angle is in I quadrant 8.) 1 cs, ct 1, angle is in II quadrant 9.) 1 tan, 1 sec 1 1, angle is in IV quadrant 10.) 7 8 sin, 8 8 cs, angle is in III quadrant 8 11.) sec, csc, angle is in II quadrant 1.) csc, ct, angle is in II quadrant 17

18 PSet ---- Algebra, Basic Trignmetry Functins 1.) sin, cs, tan, csc, sec, ct 1 1.) sin, cs, tan, csc, sec, ct 1.) sin, cs, tan 1, csc, sec, ct 1 1.) sin, cs, tan, csc, sec, ct 18

19 PSet ---- Algebra, Basic Trignmetry Functins VI. FIND ANGLES The pint is n the terminal side f an angle in standard psitin. Give the smallest psitive angle measure in bth degrees and radians. 1.) (,1).) ( 1, ).) (, 1).) ( 1, 1).) (, ).) (, ) N calculatr sectin, Find the angle [0, ). Write answers in radians. Leave the results in terms f. 7.) sin 1 19

20 PSet ---- Algebra, Basic Trignmetry Functins 8.) cs 9.) csc 10.) sec 11.) ct 1 1.) tan Calculatr sectin. Find the angle [0,0 ). Write answers in degrees. Rund the results t nearest hundredth. 1.) sin ) sin ) cs 087 0

21 PSet ---- Algebra, Basic Trignmetry Functins 1.) cs ) tan ) csc 79 Calculatr sectin. Find the angle [0, ). Write answers in radians. Rund the results t nearest thusandth. 19.) cs ) tan ) sin ) tan 8. 1.) ct. 71.) ct

22 PSet ---- Algebra, Basic Trignmetry Functins Answers 1.) 0, 11.) 7,.) 10, 1.),.) 97, ).99, 1.01.) 1,.) 1,.), ) 7 11, 7 8.), 9.), 10.), 1.) 19, 1.) 9.00, ) 10.00, ) 90., ) 190, 0 19.) 0.17, ) 0.87, ).87,..) 1.9,. 8.) 0.17,..).78,. 0

23 PSet ---- Algebra, Basic Trignmetry Functins VII. REDUCE TRIG EXPRESSION TO EQUIVALENT EXPRESSION USING REFERENCE ANGLES N calculatr sectin. Reduce t equivalent expressin using reference angles 1.) ct 1.) sec 8.) tan 11.) csc 17.) sin.) cs 19 7.) tan 11 8.) ct 7 9.) csc 9 10.) sin ) ct 1.) sin

24 PSet ---- Algebra, Basic Trignmetry Functins Answers 1.).).).).) ct sec tan csc sin.) cs0 7.) 8.) 9.) 10.) 11.) tan ct csc sin ct 1.) sin( )

25 PSet ---- Algebra, Basic Trignmetry Functins VIII. EVALUATE TRIG FUNCTION WITH SPECIAL ANGLES N calculatr sectin. Find the values. 1.) cs 10.) sec.) 7 ct 11.) 19 sec.) sin 1.) sin.) tan 1.) tan.) csc 1.) 7 csc.) sec 1.) cs 7.) cs 1.) 11 ct 8.) csc0 17.) csc 9.) ct 18.) tan

26 PSet ---- Algebra, Basic Trignmetry Functins 19.) sec 9.) 1 cs 0.) sin 0 0.) 1 sin 1.) tan 1.) csc.) 0 csc1.) 17 cs.) cs.) 19 ct.) 11 ct.) tan 70.) sec 180.) sin 0.).) 9 sec 00 ct 7.) 7 sec 7.) sin 8.) tan 0 8.) csc

27 PSet ---- Algebra, Trignmetry Functins Number --- I. GRAPH SINE AND COSINE FUNCTIONS General frm: y Asin Bx h, y Acs Bx h Fr sine and csine, BT, where T is the perid. The frequency f 1 T Graph each functin. Label the critical pints. 1.) y sinx Amplitude A Vertical Translatin Hrizntal Shrin/Stretch B Perid T Hrizntal Translatin h _ Incremental Change T x sin Bx h r cs Bx h h h h h h Asin Bx h r Acs Bx h y Asin Bx h r y Acs Bx h

28 PSet ---- Algebra, Trignmetry Functins.) y csx Amplitude A Vertical Translatin Hrizntal Shrin/Stretch B Perid T Hrizntal Translatin h _ Incremental Change T x sin Bx h r cs Bx h h h h h h Asin Bx h r Acs Bx h y Asin Bx h r y Acs Bx h.) y sinx Amplitude A Vertical Translatin Hrizntal Shrin/Stretch B Perid T Hrizntal Translatin h _ Incremental Change T x sin Bx h r cs Bx h h h h h h Asin Bx h r Acs Bx h y Asin Bx h r y Acs Bx h

29 PSet ---- Algebra, Trignmetry Functins.) y csx Amplitude A Vertical Translatin Hrizntal Shrin/Stretch B Perid T Hrizntal Translatin h _ Incremental Change T x sin Bx h r cs Bx h h h h h h.) y sinx1 Asin Bx h r Acs Bx h y Asin Bx h r y Acs Bx h Amplitude A Vertical Translatin Hrizntal Shrin/Stretch B Perid T Hrizntal Translatin h _ Incremental Change T x sin Bx h r cs Bx h h h h h h Asin Bx h r Acs Bx h y Asin Bx h r y Acs Bx h

30 PSet ---- Algebra, Trignmetry Functins 1.) y cs x 1 Amplitude A Vertical Translatin Hrizntal Shrin/Stretch B Perid T Hrizntal Translatin h _ Incremental Change T x sin Bx h r cs Bx h h h h h h Asin Bx h r Acs Bx h y Asin Bx h r y Acs Bx h 7.) y sinx 1 Amplitude A Vertical Translatin Hrizntal Shrin/Stretch B Perid T Hrizntal Translatin h _ Incremental Change T x sin Bx h r cs Bx h h h h h h Asin Bx h r Acs Bx h y Asin Bx h r y Acs Bx h

31 PSet ---- Algebra, Trignmetry Functins 7.) y sin x Amplitude A Vertical Translatin Hrizntal Shrin/Stretch B Perid T Hrizntal Translatin h _ Incremental Change T x sin Bx h r cs Bx h h h h h h Asin Bx h r Acs Bx h y Asin Bx h r y Acs Bx h 1 8.) y sin x 1 Amplitude A Vertical Translatin Hrizntal Shrin/Stretch B Perid T Hrizntal Translatin h _ Incremental Change T x sin Bx h r cs Bx h Asin Bx h r Acs Bx h y Asin Bx h r y Acs Bx h h h h h h

32 PSet ---- Algebra, Trignmetry Functins 1 9.) y sin x Amplitude A Vertical Translatin Hrizntal Shrin/Stretch B Perid T Hrizntal Translatin h _ Incremental Change T x sin Bx h r cs Bx h h h h h h Asin Bx h r Acs Bx h y Asin Bx h r y Acs Bx h 10.) y csx Amplitude A Vertical Translatin Hrizntal Shrin/Stretch B Perid T Hrizntal Translatin h _ Incremental Change T x sin Bx h r cs Bx h Asin Bx h r Acs Bx h y Asin Bx h r y Acs Bx h h h h h h

33 PSet ---- Algebra, Trignmetry Functins 11.) y sin x 1 Amplitude A Vertical Translatin Hrizntal Shrin/Stretch B Perid T Hrizntal Translatin h _ Incremental Change T x sin Bx h r cs Bx h h h h h h Asin Bx h r Acs Bx h y Asin Bx h r y Acs Bx h 1.) 1 y cs x Amplitude A Vertical Translatin Hrizntal Shrin/Stretch B Perid T Hrizntal Translatin h _ Incremental Change T x sin Bx h r cs Bx h Asin Bx h r Acs Bx h y Asin Bx h r y Acs Bx h h h h h h

34 PSet ---- Algebra, Trignmetry Functins II. CONTRUCT SINUSOIDAL FUNCTIONS Let M be the maximum value and m be the minimum value. The general frms f sinusidal functins are y Asin Bx h r y Acs Bx h Where M m 1.) A, the half f the range M m.), is the midline f the graph.) Perid T ~ time interval f a single cycle f the peridic functin.) BT r B, B r is the angular velcity, the frequency T.) h is the phase shift f the graph. f 1 T Cnstruct each sinusidal functin frm the given graph. Use h as the clsest values t the rigin. 1.) Write in the frm f y A Bx h sin Maximum Value M Minimum Value m Amplitude A Vertical Translatin Perid T Angular Velcity B Incremental Change T Phase Shift h

35 PSet ---- Algebra, Basic Trignmetry Functins.) Write in the frm f y A Bx h cs Page Maximum Value M Minimum Value m Amplitude A Vertical Translatin Perid T Angular Velcity B Incremental Change T Phase Shift h.) Given the graph, find the functin. Maximum Value M Minimum Value m Amplitude A Vertical Translatin Perid T Angular Velcity B Incremental Change T Phase Shift h

36 PSet ---- Algebra, Basic Trignmetry Functins.) Given the graph, find the functin. Page Maximum Value M Minimum Value m Amplitude A Vertical Translatin Perid T.) Cnstruct a sinusid with perid and amplitude that ges thrugh,0.

37 PSet ---- Algebra, Trignmetry Functins.) Rewrite the functin, cs. y sinx 1, shwn belw, in terms f sin, cs and y y y 7.) A ferris wheel 0 ft in diameter maes ne revlutin every 0 sec. If the center f the wheel is 0 ft abve the grund, hw lng after reaching the lw pint is a rider 0 ft abve the grund?

38 PSet ---- Algebra, Trignmetry Functins 8.) One particular July th in Galvestn, TX, high tide ccurred at 9: A.M. At that time the water at the end f 1 st Street Pier was.7 meters deep. Lw tide ccurred at :8 P.M., at which time the water was nly.1 meters deep. Assume that the depth f the water is a sinusidal functin f time with a perid f half a lunar day (abut 1 hurs minutes.) a.) At what time n the th f July did the first lw tide ccur? b.) What was the apprximate depth f the water at :00 A.M. and at :00 P.M. that day? c.) What was the first time n July th when the water was. meters deep?

39 PSet ---- Algebra, Trignmetry Functins III. GRAPH SECANT AND COSECANT FUNCTIONS Graph each functin. Label the critical pints, vertical asympttes. 1.) 1 ycsc x1 The reciprcal functin y Amplitude A Vertical Translatin Hrizntal Shrin/Stretch B Perid T Hrizntal Translatin h _ Incremental Change T.) y sec x The reciprcal functin y Amplitude A Vertical Translatin Hrizntal Shrin/Stretch B Perid T Hrizntal Translatin h _ Incremental Change T

40 PSet ---- Algebra, Trignmetry Functins.) y sec x 1 The reciprcal functin y Amplitude A Vertical Translatin Hrizntal Shrin/Stretch B Perid T Hrizntal Translatin h _ Incremental Change T 1 sec.) y x The reciprcal functin y Amplitude A Vertical Translatin Hrizntal Shrin/Stretch B Perid T Hrizntal Translatin h _ Incremental Change T.) y cscx 1 The reciprcal functin y Amplitude A Vertical Translatin Hrizntal Shrin/Stretch B Perid T Hrizntal Translatin h _ Incremental Change T Answers

41 PSet ---- Algebra, Trignmetry Functins II 1.) y sin x.) y cs x 1.).).) y sin(10x 0).) 7.) 1.90 sec. 8.) a.) : A.M., b.).1 meters, c.) 1:18 A.M.

Precalculus A. Semester Exam Review

Precalculus A. Semester Exam Review Precalculus A 015-016 MCPS 015 016 1 The semester A eaminatin fr Precalculus cnsists f tw parts. Part 1 is selected respnse n which a calculatr will NOT be allwed. Part is shrt answer n which a calculatr