MAT 172 Exam Review Worked out Problems

Exam Review - Solutions MAT 172 S=15 ft I5 ==316 3/5 r 25 rodians 2. 27 (100) = 300 = 72° 5 S 3 Sin 6.5 CSC 6.5 Sintes Π 40 4. tan = cot (-5) 20 cot (9) 20 = 5. 15 12 Sin=1 H 124 5 b e 16. pend ==== 3 の 3 8 7. phase shift = shift=-=-= 2 b 2 8. Cos' S X X a A 30° or Ⅱ 9. Sin 15° 30 Sin (45-30) Sin 45 cos 30 - Sin30 cos45 2 2 2 -2 2 does not match Answer Key 10. Cos(a+b) = Cosa CoSB -15 20 29 300 493 -Sind sing 21 29 168 493 -()() LI 132 493 ۰ Sin = 21 10 be 29 21 20 Cos 20 = sin' - COS 441 841 400 841 e ()() -41 841 12. 8( o * s ^ 2 * x 8((1 + cos 2y)/2) = 4(1+cos 2x) sqrt -1+11 cos 71 = 4 + 4cos 2x 13. Sin aa.s Sin(45/2) = plus/minus sqrt((1 - cos 45 deg)/2) =+ sqrt 1 - (sqrt(2))/2 = sqrt(2/2 - (sqrt(2))/2) * 2 = sqrt((2 - sqrt(2))/2) = sqrt((2 - sqrt(2))/2 * 1/2) = sqrt((2 - sqrt(2))/4) 4. 11 A 20 B 11/(Sin * 20) = a/(Sin * 4S) alpha = 32.7 C Sin ||5 = || sin 20 not same on ans. key. angle A = 45 a = aa * 0.7 c = 29.1 15. (-^ - 1 , 2 pi 4 ) x = r * cos theta = - 7(cos((3pi)/4)) = (9sqrt(2))/2 y = v * sin theta = - 7(sin((3pi)/4)) = (sqrt(2))/2 12/2 45 - (sqrt(2))/2 135 ((7sqrt(2))/2, - (7sqrt(2))/2) 16. x ^ a + y ^ a - 4x = 0 r ^ 2 - 4(r * cos theta) = 0 r ^ 2 - 4r * cos theta = 0 r(r - 4cos theta) = 0 r = 0 v = 4cos theta pole 17. r = 10sin theta ro or r ^ 2 = 10r * sin theta x ^ 2 + y ^ 2 = 10x 1 x ^ 2 - 10x + y ^ 2 = 0 18. omit z = 3(cos pi/3 * i * sin(pi/3)) = 3 * [[1/2, i, (sqrt(3))/2]] =1 overline 3/2 + i * (3sqrt(3))/2 160 1/2 (sqrt(3))/(2r) 20 5.4 (C0s 20+10 ti sin 2010) d * 0(cos 30 deg + i * sin 30 deg) 21. = 8/3 * (cos(pi/2 - pi/6) + i * sin(pi/2 - pi/6)) = 8 3 ( cos(pi/3) + (s * sin(pi/3)) 22. vec u Rightarrow(2-0)i+(-2-2)j Rightarrow 2i - 4j vec v Rightarrow(5-3)i+(-4-0)j Rightarrow 2i - 4j ✓ || vec u ||= sqrt(a ^ 2 + (- 4) ^ 2) = sqrt(4 + 16) = 2sqrt(15) 23. vec v =(-1-4)i+ boxed - 5i - 9j (-6-3)j 24. ||u + v|| = ||7i + 2j|| = sqrt(72) + 2 ^ 2 = sqrt(149) + 4 as, ||v|| = sqrt((- 3) ^ 2 + (- 4) ^ 2) = sqrt 9 + 16 = sqrt(25) = 5 - 3/5 * i - 4/5 * j 26. 10 20 b = 10sin 120 deg = 10((sqrt(3))/2) = 5/3 a = 10cos 120 deg =10(-^ 1 /2)=-S V = - 5i + 5sqrt(3) * j sqrt(53) (sqrt(3))/2 1/2 27. sin t = 1/4 Si * n ^ 2 * t + cos^2 t = 1 (4)² + cost=1 2 1/16 + cos^2 t = 1 sqrt cos^ 2 L- Gamma E co * 5t = sqrt(15/16) Cost = (sqrt(15))/4 28. tan 1 pi/6 - sin(pi/3) 1/2/((sqrt(3))/2) - (sqrt(3))/2 60 30 (2/2) * (sqrt(3))/3 - ((3sqrt(3))/3 = (3sqrt(3) - 3sqrt(3))/6) = boxed - sqrt 3 6 29. mathcal COS[ ((2 * pi')/3 + a) +(- 2. pi^ prime 3 -a)] cos(- (4pi)/3) 30. (9,)→(-9,-)~(9) (9,) -9315 12 31. (2,-2) (2sqrt(2), - 4S ^ d) 2 -2 r^ prime prime = sqrt(a ^ 2 + b ^ 2) r = sqrt((z) ^ 2 + (- z) ^ 2) = sqrt(4 + 4) = sqrt(8) = 2sqrt(2) tan theta = - 2/2 tan theta = - 1 32. Theta = (5pi)/6 tan((5pi)/6) = y/x 1/2/((- sqrt(3))/2) = y/y 30 (- sqrt(5))/2 150 (- sqrt(3))/3 = - 1/(sqrt(3)) = y/x y = (- sqrt(3))/3 * x (- sqrt(3))/3 = 4/x (3y)/3 = (- sqrt(3) * x)/3 33. 13 140 p ^ prime1 X Sin 27-127 X x = a' * 79 ft 34. y = cos x Am*rho = I Per ==2=2ㅠ -2TT (- 3pi)/2 -11 0 11/2 3 * T deg ) 211 35. A 109 10 9 C B a=90+10°-2(9)×(10) Cos 109 a ^ 2 = 239.6 a = 15.8 angle C = 35.6 deg angle B = 35.2 a = 15.8 10 ^ 2 = 9 ^ 2 + 15.8 ^ 2 - 2(9)(6.8) * cos c 100 = 330.64 - 284.4cos c - 230.64 = - 284.4cos c 81097 = cos c 35.6 = C 36. Center (0,0) FOCi= sqrt(81 - 49) = sqrt(32) = 5.7 37. center (0,0) (x ^ a)/4 + (y ^ a)/4 = 1 Fbc 1 =( matrix 0&12 sqrt 3 )\\ (0, - 2sqrt(3)) matrix 70c * sqrt(1b - 4) = sqrt(12) = 2sqrt(3) 38 11011011111111011914 (x ^ 2)/64 + (y ^ 2)/39 = 1 aligned C= sqrt a^ 2 -b^ 2 \\ sigma= sqrt 1041 - b ^ 2 aligned b ^ 2 = 37 39. (4 * (x - 1) ^ 8)/36 + (9 * (y + 1) ^ 2)/36 = 36/36 ((x - 1) ^ 2)/9 + ((y + 1) ^ 2)/H = 1 Center (1-1 E A 00 Foci = sqrt(9) - 4 S (3.2,-1) (-1,2,-1) Al. (36x)/324 ^ 2 - (9y ^ 2)/(3ay) = 324/324 (x ^ 2)/a - (y ^ 2)/36 = 1 HOTT 11011 1= ±m(x-n)+k = ±(x-0)+B y = plus/minus 2 * x y = 2x y = - 2x 42. 43. cote=, cos theta < 0 2 CSCD= 2 S A X CSLO Sin H (2) ^ 2 + (- 1) ^ 2 = C ^ 2 4 + 49 = c ^ 2 53 = c ^ 2 sqrt(53) - c (sqrt(53))/2 44. see (tan A 3 X 1 Inverse tanger X 1/2/((sqrt(5))/2) * 1/2 * 2/(sqrt(3)) = 1/(sqrt(3)) = (sqrt(3))/23 Sec = H A 2 B 213 3 45. A = 38° b= 14m C = lam Area=bcsin A. A 1438 12 C B (14)(12)sin38 51.7 52 m2