Name c V2M0W1H7O MKwuYtxaa ]SooUfBt[wEaxrYed alxlkcb.a K NAMlFlH qrniig\hltosf Fr`eVsJeSryvze_dX. -1-

Transcription

1 Precalculus Name c VM0W1H7O MKwuYtxaa ]SooUfBt[wEaxrYed alxlkcb.a K NAMlFlH qrniig\hltosf Fr`eVsJeSryvze_dX. Vectors Test Review Find the exact value of each trigonometric function. 1) cos 15 ) cos 10 Date Period ) tan 10 4) tan 60 5) tan 15 6) sin ) cos -70 8) sin -660 Use the given point on the terminal side of angle q to find the value of the trigonometric function indicated. 9) cos q ; (-9, 19) Find the exact values of the two trigonometric ratios not given. 10) tan q = - 0 and cos q > 0 1 t WS0a1z7o dkhuntka^ ^SXoBfgtTwQa\rNeG QLPLbCA.Z f KAZlGlz xrkipgphxtjsv ArGeKs\eersvkejd`.N n gmcapddes ]wfi^trhq liqnzfiiunsi_teeu npvrienceasldczunlbussc. -1-

2 Find the component form of the resultant vector. 11) Given: A = (-10, -6) B = (4, 9) C = (1, 5) D = (-5, 9) Find: -AB - CD Express the resultant vector as a linear combination of unit vectors i and j. 1) Given: A = (-5, 1) B = (6, ) C = (7, -9) D = (-10, 0) Find: AB - CD Find the component form of the resultant vector. 1) a = -1, - g = 8, 1 Find: -4a + 8g Express the resultant vector as a linear combination of unit vectors i and j. 14) u = i - j g = 4i + 7j Find: 6u - 5g 15) Given: P = (-, 10) Q = (-1, -) Find the vector opposite PQ 16) Given: A = (-, -10) B = (8, -9) Find: 10AB Draw a diagram to illustrate the horizontal and vertical components of the vector. Then find the magnitude of each component. 17) m = 0, 16 d pk0l1z7n BKKuUt[aQ ZS^oSfUtTwlaorbeB FLlLBC[.z e raqlald Lrji\gjhBtOsu `rrefsyewrnvcetdr.t _ PMPa`dDex AwgiXtYhN QIrnCfpihnriwtMed MPErHekc[a_lucIuClbutsz. --

3 Draw a vector diagram to find the resultant of each pair of vectors using the triangle method. Then state the magnitude and direction angle of the resultant. 18) t = 16, 10 u = 1, ) t = -15, 5 u = 9, -1 Find the following information for each vector, if not provided in the question: Linear combination, magnitude and direction angle. 0) v = -9, 16 1) k = 50, 1 Draw a vector diagram to find the resultant of each pair of vectors using the triangle method. Then state the magnitude and direction angle of the resultant. ) t = -8, 15 u = 18, 14 F _I0Y1k7f `KuuetNa\ qscoufitzwxaprhem OL\LNCh.O I GAclUly HrZivgChMtRsF FrEeisOeGrWvdemdI.U U nmuagdle^ qwfiqtshp uicnbfgivnyi[tieu spyrzefcraclmcpuslmu^sl. --

4 ) m = -8, -15 n = 7, Find the dot product of the given vectors. 4) u = -5, -1 v = -1, -9 Find the measure of the angle between the two vectors. 5) u = -i + 5j v = 9i - 8j 6) u = -, 7 v = 9, 8 State if the two vectors are parallel, orthogonal, or neither. 7) u = 1i - 15j v = -5i - 7j 8) u = -7, -1 v = -8, -4 D ]G0b1f7I rkcustqaj `SEoffctMwyairoec [LsLxC`.y K DAWlVlS XrLihgqhJtisG WrGe_sneArevDetdm.q a CMHaDdUeB gwdittshz ei\noftinniiptdev ZP[r\eJcHaclFcquNlRuFsP. -4-

5 Precalculus Name X px0y1h7a HKmuht\ad gsoowfgtpw[ayraej klplqcz.a K AAplIli NrKirguhYtMsd graeusdehrxveeudk. Vectors Test Review Find the exact value of each trigonometric function. Date Period 1) cos 15 ) cos 10 - ) tan 10 4) tan 60 5) tan ) sin ) cos ) sin -660 Use the given point on the terminal side of angle q to find the value of the trigonometric function indicated. 9) cos q ; (-9, 19) Find the exact values of the two trigonometric ratios not given. 10) tan q = - 0 and cos q > 0 1 sin q = , cos q =, tan q = csc q = - 9 9, sec q = 0 1 ` tp0i1z7t CKVuvttaI NSRoTfSt[w]aSrBeK dlilhcz.w a EAPlflv NrDigg[hStHsN frsedsxe_rhvieqdr.^ G PMHaBdMeh ]wtiktghe CIxnffviunYidtlem UPYrwesceaPlKcjuIlouisB. -1-

6 Find the component form of the resultant vector. 11) Given: A = (-10, -6) B = (4, 9) C = (1, 5) D = (-5, 9) Find: -AB - CD -8, -19 Express the resultant vector as a linear combination of unit vectors i and j. 1) Given: A = (-5, 1) B = (6, ) C = (7, -9) D = (-10, 0) Find: AB - CD 8i - 8j Find the component form of the resultant vector. 1) a = -1, - g = 8, 1 Find: -4a + 8g 68, 108 Express the resultant vector as a linear combination of unit vectors i and j. 14) u = i - j g = 4i + 7j Find: 6u - 5g -8i - 5j 15) Given: P = (-, 10) Q = (-1, -) Find the vector opposite PQ -i + 1j 16) Given: A = (-, -10) B = (8, -9) Find: 10AB 110i + 10j Draw a diagram to illustrate the horizontal and vertical components of the vector. Then find the magnitude of each component. 17) m = 0, 16 x m y Horizontal: 1.58 Vertical: B lh0x1b7z AKXudtFa_ JSOorfktrwOaOrueU dljlyc`.w ] SAZlvlw JrZimgYhStFsy arsevsqecr`v]eudo.n X gm]atd\e` xwdiqtwhf [IHn^f\ianwiMtler XPqrSePcxaVlvcZuhluuHs\. --

7 Draw a vector diagram to find the resultant of each pair of vectors using the triangle method. Then state the magnitude and direction angle of the resultant. 18) t = 16, 10 u = 1, ) t = -15, 5 u = 9, -1 t u u t t + u 8.64; ; 9.4 t + u Find the following information for each vector, if not provided in the question: Linear combination, magnitude and direction angle. 0) v = -9, 16-9i + 16j 1097» ) k = 50, i - 7.j Draw a vector diagram to find the resultant of each pair of vectors using the triangle method. Then state the magnitude and direction angle of the resultant. ) t = -8, 15 u = 18, 14 u t + u t 0.68; I IO0E1h7B skkuvtdan PS\osf]tFwbanr]eV ZLFL\Cn.n J daelcle oreiogbhutbsp wraeisyeyrnvbezdw.n L QMcacdaef ewsiqtbhb GIJnSf\iZnSiltMes _PwrTe\cWaGlNcquzlOu]s^. --

8 ) m = -8, -15 n = 7, m m + n n 1.04; 65.4 Find the dot product of the given vectors. 4) u = -5, -1 v = -1, Find the measure of the angle between the two vectors. 5) u = -i + 5j v = 9i - 8j ) u = -, 7 v = 9, State if the two vectors are parallel, orthogonal, or neither. 7) u = 1i - 15j v = -5i - 7j Orthogonal 8) u = -7, -1 v = -8, -4 Parallel h w\0w1v7g dkiu_tlai ysnotfzthwbamrse` plul\cn.t b VAulGl\ prfilgihpt]sq arwevslevrjvqewdl.n Z nmmacduew jwiigtchw UIenYfyiLnbiztSel JPfr`eWcua\l\cZuQlfuzsp. -4-