Trigonometry Semester Review a pam productions review packet. 9. In the diagram, circle P is a unit circle. If point B is located at 2 π, what are the

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1 Trignmetr Semester Review a pam prductins review packet. Find the degree measure f an angle that measures 7 6 radians.. What is the radian measure f an angle that has degree measure 675?. What is the radian measure f an angle that has degree measure 80?. What is the radian measure f an angle that has measure 0? 5. If θ has measure 000, then which is a cterminal angle α such that 0 α < 60? C. 78 D I. sin 0 II. sin III. tan IV. cs Which f the abve values are equal? I, III, IV nl II, III nl C. I, IV nl D. III, IV nl 7. Give the quadrant that has the fllwing signs. cs > 0, sin < 0 r. I s. II t. III u. IV sin > 0, tan < 0 r. I s. II t. III u. IV 8. What is the perid f the graph f = 5sin( )? 5-5 t 5 C. D. 9. In the diagram, circle P is a unit circle. If pint B is lcated at, what are the crdinates f pint B? B, P, C., D., 0. In the diagram, circle P is a unit circle. If pint B is lcated at 7, what are the crdinates f pint B?,, C., D.,. The terminal side f angle θ in standard psitin cntains the pint ( 5, ). Give the csθ as a reduced fractin.. The terminal side f angle θ in standard psitin cntains the pint (6, 8). Give the cscθ as a reduced fractin. P B Page f 8 created Jul 0

2 Trignmetr Semester Review a pam prductins review packet 0. If csθ = and 0 < θ <, then 9 what is the value f tanθ? C. 0 D Fr 0 < 60 and sin = 0.6 then which gives the apprimate values f? {0.590, 79.0} {0.0, } C. {9., 9.} D. {9., 0.876} E. {68.8,.77} 5. B t a A b T 7. What is the eact value f each? NO DECIMALS! cs0 sin C. tan 690 D. ct E. csc F. sin 0 8. In a rectangle with sides and 6, find the smallest acute angle in the diagram, t the nearest degree. 9 7 C. 5 D.? 6 In the abve diagram, if m T = 7 and a = then find the value f b t the nearest tenth place. R. 9. S. 9. T. 0.0 U.. 6. A blt f lightning hit m tree and a limb fell s that it leaned against m huse. The tp f the limb hit m windw, feet high and the base f the limb was n the grund 0 feet frm the huse. What acute angle did the limb make with the grund, t the nearest degree? 6 C. 7 D / / = msin( ) + n wheeeee! What is the amplitude and vertical shift f the graph shwn? Page f 8 created Jul 0

3 Trignmetr Semester Review a pam prductins review packet 0. Label each frm these chices: = sin, = cs, = tan, = csc, = sec, = ct (Ignre the wildlife. ) Graph Graph / / / / Graph 5 Graph / / / / Graph 6 Graph / / / / /. What are the minimum and maimum values f each? = 0 cs(5 ) has ma and min. = 6sin( ) + has ma and min. Page f 8 created Jul 0

4 Trignmetr Semester Review a pam prductins review packet. Fr each item belw, give answers in eact fractinal frm, and be careful f the restrictins n the ranges f the arcfunctins.. If What is What is What is 5 arccs sin 6? arcsin sin? cstan 5? 8 sinθ = and θ then give 5 sin θ. C. D the value f ( ). If sinθ = then give the value f 5 cs θ in fractin frm. 5. ( ) R 65 S 5 6. If sinθ = 0.09 and 0 θ < 60 then t the nearest tenth f a degree, θ = 5. r r 5.7 C. 7.7 r 85. D.. r A ninja sparring ple is 0 ft lng and is leaning against a wall. The base f the ple is feet frm the base f the wall. What is the angle that the ple makes (t the nearest tenth f a degree) with the grund? C.. D The ninja sparring ple is still 0 feet lng and is still leaning against the wall. If the ple makes an angle f 7 with the grund, hw far up the wall is the tp f the ple, t the nearest tenth? 6.5' 6.6' C. 9.0' D..0' 9. Which is equivalent t sin(0)? sin 0 sin 60 C. sin 0 D. sin Which is equivalent t cs00? cs 60 cs0 C. cs 60 D. cs0 T If ST=, m R= 65 and m S = 5 then give the length RS t the nearest tenth place. Page f 8 created Jul 0

5 Trignmetr Semester Review a pam prductins review packet. Fr 0 < < 90 5 and sin = then sin( ) = r cs( ) r. 9 C. s t s. 9 t cssin = 5 5 r. s. t. u u In each triangle belw, hw man slutins are there? AB= cm, AC= 0 cm, and m B= 0 has pssible slutins. c=0 m, b=5 m, m B= has pssible slutins. C. a= cm, c= cm, m A= 8 has pssible slutins.. cstan = 0 0 sin tan 0 C = C. 5 5 D. Arc Arc 0 0 D Find the area f triangle RST, t the nearest tenth f a square cm: r=0 cm, s=0 cm, m T = cm 0 5. cm a Give the value f a, the side length. 7. Frm the tp f a tall building, Hectr sees his lst dg n the grund at an angle ff the hrizntal f 0 degrees. The dg's name is Fred, but that is irrelevant. The dg is 56 ards directl frm Hectr's ees; he knws this frm instinct. T the nearest ard, hw far frm the base f the building is the dg (Fred)? ds 5 ds C. 65 ds D. 96 ds 8. A wman is standing n the grund, 00 feet frm the base f a building. If the angle ff the hrizntal at the feet f the wman t the tp f the building is 50 degrees, hw tall is the building, t the nearest ft? 58 ft 5 ft C. 9 ft D. 0 ft 9. Beauregard ntices a bear traveling n a bearing (s apprpriate, dn t u think?) f 56 and a bar traveling at a bearing f 00. "B" u cnfused et? Find the angle between the line f sight f the bar and the line f sight f the bear. Beauregard's Bear abslutel adres alliteratin. Page 5 f 8 created Jul 0

6 Trignmetr Semester Review a pam prductins review packet 0. Simplif each f the fllwing: sinθctθ r. csθ s. t. - u. tanθ sin θ + cs θ r. csθ s. t. - u. tanθ C. + tanθ tanθ r. sec θ s. t. - u. tanθ D. secθsinθ r. csθ s. t. - u. tanθ E. ctθ tanθ r. csθ s. t. - u. tanθ. Match (sme chices ma be used mre than nce). cs( θ ). csθ cs( θ). sinθ C. sin(90 θ ) D. sin(80 θ ). csθ. sinθ. If sin = and < < then cs = 5 C. D. 6. = sin( ) sin cs C. sin D. cs. sin(90 + ) = sin cs C. sin D. cs 5. If sin u = fr 5 0 cs v = fr 9 0 < u < and 0 < v < then find cs( u+ v) (fractin frm!) sin( u v) (fractin frm!) 6. Use an identit t simplif: sin cs cs6 sin6 C. cs 6 D. sin 6 7. Find B A if A = ( 5i + j) and B= i+ 6j. 8. What is the directin angle fr each vectr belw? i+ j r. 0 s. 60 t. 0 u. 50 8i 8 j r. 0 s. 60 t. 00 u. 0 C. 6i 6j r. 5 s. 5 t. 5 u What is the angle between the vectrs i 5j and 0i+ j, t the nearest degree. 50. Use an identit t simplif: cs sin cs6 sin6 C. cs 6 D. sin 6 Page 6 f 8 created Jul 0

7 Trignmetr Semester Review a pam prductins review packet 5. What is the dt prduct, AB g, f the vectrs A= i 5j and B=0i+ j? 5. What is the value f k s that the vectr 9i j is rthgnal t i + kj? 5. Give the unit vectr with the same directin as each vectr belw. 59. Simplif ver the cmple numbers: i r. i s. i t. u. - i 7 r. i s. i t. u. - C. (5 i) + ( i) 8i 8 j 6i 8j 5. Write a vectr f length 6 with the same directin as the vectr 5i j. 0i j 65i 56 j C. 6i 6 j D. i j 60. D. 5 i r. s. i t. 5 + i u = r. i s. 5 7i t. 5+ 7i u Graph the fllwing n the real imaginar plane. (nt multiple chice!) i i C. + i D. 57. ( + i)( i) = r. 8 i s. 8+ i t. + i u. 5+ i On the grid abve, graph the plar crdinates, and label it, and label it 6 C., and label it C. 58. ( ) 6 i = 6 + 6i C. 096 D. 096i 6. Write in rectangular crdinates, runded t the nearest hundredth place. 8 5, Page 7 f 8 created Jul 0

8 Trignmetr Semester Review a pam prductins review packet 6. Simplif: ( i) i 6 6 i C i D. 6 6i cis cis 6 = 5 0cis 8 9cis 6 5 C. 9cis D. 0cis Write in plar crdinates, using radians. 65. ( 0,0). 6 0 Beauregard's bar is hiding in a triangle. He is scared f bears. If the triangle has sides 6 feet, ft and 0 feet. Hw man square feet are inside the bar's burrw? Rund t the nearest square ft. 7 5 C. 8 D. 89 Page 8 f 8 created Jul 0