Date Period In each problem, angle C is a right angle. Solve each triangle rounding answers to the nearest tenth. 12) sec 29p 6

Transcription

1 Pre Calc T YV0X1^S IKQuZtIal ]SEoofttCwIa_rZeq oltlaci.n T gaolslu ErEi]gjhkt[s\ Ar\efsQe_rsvoeXdM. Trig Review Name Date Period In each problem, angle C is a right angle. Solve each triangle rounding answers to the nearest tenth. 1) b = 8, a = 7 ) m B = 58, c = 9 Find the values of all trig functions of q from the given information. Rationalize all denominators. ) tan q = 15 ; terminal point of q is in 8 quadrant III 4) cos q = ; sin q > 0 Find the exact value of each trigonometric function. 5) sec -15 ) sin 5 7) sin 40 8) cot ) sec ) tan - 5p 11) csc - 1p ) sec 9p c `]0y1hl BK\uWtIax DSGozfCtXw^aGr_eo xl`loce.s Q danlslt `reiagxh^tfsr wraeasbeqrgvhejda.t t umaaedser rw[ipt[hp fidnqfnienfi\t_eg OASlhg]e]bLr\aw si.

2 Solve each triangle. Round your answers to the nearest tenth. 1) b = 17, c = 10, a = 11 14) In DEF, f =, m D = 9, e = 10 15) In ABC, m A = 145, c = 0, a = 17 1) In XYZ, m X = 41, z =, x = 7 Find the area of this triangle to the nearest tenth. 17) In EFD, d = 4 mi, e = 11. mi, m E = ) A triangle has an area of.8 square inches, and two of the sides of the triangle have lengths 9. inches and 7.4 inches. Find the smallest angle in such a triangle. 19) A triangular field has sides of lengths 8, 9, and 4 ft. Find the largest angle. Find the exact value of each. 0) cos 15 1) sin 1p Assuming sin x = 4 5 if p 5 < x < p and cot y = - if p < y < p ) tan ( x + y ) ) sin ( x - y ) 4) csc ( x + y ) 5) sec ( x - y ) v vy0j1lg DKeuItqaY NSjo^f\towhaYrke[ fl^lcce.b k pahlrlr prrikgkhftis^ prxe]s`evrmvbeedx.c i hmoakdces KweintzhS oiznofsiwnliytiev XAMl]gKetbPr^aL bc.

3 Use a double-angle identity to find the exact value of each expression. ) cos q = - 4 and 90 < q < Find tan q 7) csc q = Find cos q and 70 < q < 0 Use a half-angle identity to find the exact value of each expression. 8) tan q = 7 and 180 < q < ) sec q = 5 4 and 70 < q < 0 Find cos q Find tan q 0) sec q = 1 and 0 < q < 90 Find sin q Find the exact value of each expression, if it is defined. Answer in both degree and radian. 1) sec -1 (- ) ) tan -1 (- ) Find the exact value of each expression, if it is defined. ) cos (tan -1 (- ) ) 4) csc (cot -1-4 ) Solve each equation for 0 q < p. 5) tan q = -1 ) cos ( q 4 + p 4 ) = - 1 S xt0t1lq BKcuwtGag QSko^fYtsw[aFrceQ mlal_cj.h L ZA`lJlj PrMikgIhFtzsU yrkegs[e]rbvsesd`.y a DMhaCdpeS _wciktfh] HIknEfgiWnCiKtTeI MATl^g^ezbRrKaa yh.

4 Solve each equation for -p q p. 7) = cos q 11p 8) sin (-q + ) = 0 Solve each equation for - p q p. 9) sin q = 1 40) tan ( -q + p 4 ) = 1 Find all solutions to each equation in radians. 41) tan q = - 4) sin ( -q + 5p ) = - 1 Find the reference angle. 4) 9p 44) - 49p 18 Find a coterminal angle between 0 and 0. 45) 99 Find a coterminal angle between 0 and p for each given angle. 4) - 5p Find a positive and a negative coterminal angle for each given angle. 47) 45 48) - 7p t Od0f1sh ckkuzthaq NSToMfVtuwPa_rHeH OLPLiCV.d E IAHl]lD Wr]iDgNhYtPsr RrYezsMesrTvreCdM.F p GMAagdKe\ uwoihtxhq GIen_fjirnViqtheH AAglEgLe_bdrBa] eh.

5 Pre Calc m da0y1ms VK_ubtBaA PSlojfvtjwTaYrcee RLTLOC\.M E FAplrl^ vrjingshqtvsz PrIedsSe^rivLegdt. Trig Review Name Date Period In each problem, angle C is a right angle. Solve each triangle rounding answers to the nearest tenth. 1) b = 8, a = 7 m B = 48.8, m A = 41., c = 10. ) m B = 58, c = 9 m A =, a = 4.8, b = 7. Find the values of all trig functions of q from the given information. Rationalize all denominators. ) tan q = 15 ; terminal point of q is in 8 quadrant III sin q = ; csc q = ; cos q = ; cot q = 8 17 ; sec q = ) cos q = ; sin q > 0 sin q = 1 1 ; csc q = 1 cot q = - ; sec q = - 1 ; tan q = - ; Find the exact value of each trigonometric function. 5) sec -15-7) sin 40 9) sec -75 ) sin 5-8) cot -540 Undefined 10) tan - 5p - 11) csc - 1p - ) sec 9p - v nd0q1ya rk`umtvat XS\oAf`t]w[ajrme[ CLTLyCM.T y VArlKlp TrWi\gYh[tOsO WrmemszeqrXv_eZdl.d U _MdaOddee ]woixtlhb FIdnif^ienDiItJeQ oadlrgfe`bnrsaa Gz.

6 Solve each triangle. Round your answers to the nearest tenth. 1) b = 17, c = 10, a = 11 m A = 8, m B = 108, m C = 4 14) In DEF, f =, m D = 9, e = 10 m E = 54.7, m F = 9., d =. 15) In ABC, m A = 145, c = 0, a = 17 Not a triangle 1) In XYZ, m X = 41, z =, x = 7 m Y = 85.7, m Z = 5., y = 41 Or m Y =., m Z =.7, y = 8.8 Find the area of this triangle to the nearest tenth. 17) In EFD, d = 4 mi, e = 11. mi, m E = mi² 18) A triangle has an area of.8 square inches, and two of the sides of the triangle have lengths 9. inches and 7.4 inches. Find the smallest angle in such a triangle ) A triangular field has sides of lengths 8, 9, and 4 ft. Find the largest angle..7 Find the exact value of each. 0) cos Assuming sin x = 4 5 if p 04 ) tan ( x + y ) 5 4) csc ( x + y ) ) sin 1p 5 < x < p and cot y = ) sin ( x - y ) if p < y < p 5 5) sec ( x - y ) - 5 J Lo0]1lr SK\uOtFab ps]ovfctrwbanrxee vlfltc[.o ] EAvlAlx ^riiqgnhdtgsn BrpeGsue\rdveeodO.f M FM[aVdTeb UwEiLthha oi[n\fwifnpixtbes taclggbekbfr\ag Lw.

7 Use a double-angle identity to find the exact value of each expression. ) cos q = - 4 and 90 < q < Find tan q ) csc q = Find cos q Use a half-angle identity to find the exact value of each expression. and 70 < q < ) tan q = 7 and 180 < q < ) sec q = 5 4 and 70 < q < 0-1 Find cos q Find tan q ) sec q = 1 and 0 < q < 90 Find sin q Find the exact value of each expression, if it is defined. Answer in both degree and radian. 1) sec -1 (- ) ) tan -1 (- ) -0, - p 15, p 4 Find the exact value of each expression, if it is defined. ) cos (tan -1 (- ) ) 1 4) csc (cot -1-4 ) 5 4 Solve each equation for 0 q < p. 5) tan q = -1 { p, 7p 4 4 } ) cos ( q 4 + p 4 ) = - 1 { 5p } Q hp0z1^c [KjuNtDae ZSCoIf]tZwca_r]eS JLgLzCU._ ` FAUlglb YrmihgMhvtEsI Xroesskekr]vLexdZ.Q P tmtaydaem awditteho tixnwfiicnbi[tzeg LARlNgZeVbzroaA Vy.

8 Solve each equation for -p q p. 7) = cos q No solution. 11p 8) sin (-q + ) = 0 {-, p 5p } Solve each equation for - p q p. 9) sin q = 1 { p } 40) tan ( -q + p 4 ) = 1 {-, - p p, p, p } Find all solutions to each equation in radians. 41) tan q = - { 11p + pn} 4) sin ( -q + 5p ) = - 1 {- - p pn, - p 9 - pn } Find the reference angle. 4) 9p 5p 44) - 49p 18 5p 18 Find a coterminal angle between 0 and 0. 45) 99 7 Find a coterminal angle between 0 and p for each given angle. 4) - 5p 1p Find a positive and a negative coterminal angle for each given angle. 47) and ) - 7p 17p and - 1p h JE0w1aq zkdurtwa` TScoBfXtpwdaArVev rlxlych.l S XA_lFlA vriizgbhctfsa _rhessrekr]vresde._ s YMJaXdeex SwYiqtzh[ MICnafniJn\iztueI NAtlsgieVbgr[as U].