MATE EXAMEN FINAL
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1 MATE7 - EXAMEN FINAL Apellidos Nombre: Instrucciones. Seleccione la alternativa que corresponde a la respuesta del problema. Encunetre el valor de la función. ) Let f() = 5. Find f(). A) 5 B) 5 C)5 D) 4 ) Resuelva el problema. ) El crecimiento de la población de un tipo de rodeador se puede describir por la función eponencial A(t) = 78e0.0t, don t representa el número de años desde el 965. Aproime la población que hubo en el año 000. A) 4 B) 569 C) 809 D) 485 ) Escriba la ecuación logarítmica como una ecuación eponencial equivalente. ) ln() = - A) e- = B) ln - = C)0- = D) e = ) Resuelva la ecuación: 4) 4- = 64 4) A) {-} B) C){} D) - 5) log = - 5) A) -6 B) 9 C) - D) 8 6) (5 - ) = 6 6) A) B) - C)8 D) 8 7) log( + 4) = 0 A) 4 B) C)0 D) - 7) Aproime a cuatro lugares decimales. 8) log A) B) -.40 C) D) ) 9) log 5 5 A).875 B) C).686 D) )
2 Use las propiedades de logarítmos para combinar términos. 0) log 8 + log 8 0) A) log 8 B) log 8 C)log 8 D) log 8 Encuentre la medidas de dos ángulos, uno positivo otro negativo, que sean coterminales con el ángulo dado. ) 56 ) A) 46 ; -4 B) 56 ; -4 C) 56 ; -04 D) 6 ; -4 ) π 7 ) A) π ; π 7 C) 5π 7 ; - π 7 5π - 60 B) 7 ;- π 7 D) 8π 7 ; - 6π 7 Indique el cuadrante en dónde se encientra el ángulo. ) 09 A) III B) I C)II ) 4) 8π 7 4) A) II B) IV C)III D) I Convierta el ángulo a grados decimales redondée a la centésima más cercana. 5) 6 9'48'' A) 6.46 B) 6.56 C) 6.50 D) 6.5 5) 6) 09 5''' A) B) C) D) ) Convierta el ángulo a grados-minutos-segundos (DMS). De ser necesario, redondée al entero más cercano los segundos. 7) ) A) 8 5'4'' B) 8 5'0'' C) 8 5'89'' D) 8 5''' 8).7 A) 46'7'' B) 4'7'' C) 44'46'' D) 4'47'' 8) Convierta la medida de grados a radianes. Use el valor de π según su calculadora redondée a tres lugares decimales. 9) 4.7 9) A).898 B) 0.5 C) 0.57 D) ) 8 49 A) B) C) D) ) ) 9 8'55'' A) 9.5 B).66 C).69 D).57 )
3 Convierta la medida de radianes a grados. Use el valor de π según su calculadora. ) 7π ) A) 54.9 B) 60 C) 60 D) 5.4π ).8977 A) 4. B).6 C).8 D). ) Aproime el largo del arco que se forma por el ángulo central α en un círculo de radio r dado. 4) r = 0.66 cm, α =.0 A) cm B) cm C) cm D) cm 4) 5) r = 96. m, α = 4π 5 5) A) 0.75 m B) m C) m D) m Encuentre el radio del círculo, dado el ángulo α el largo del arco s. 6) s = 7.9 ft, α = π 7 6) A) π 55. ft B) 55.π ft C)0.6π ft D) 55. π ft 7) s = 4cm, α = 4 A) 60 cm π 0 B) π cm C) cm 0 D) π cm 7) Encuentre el valor eacto. 8) sin (0 ) A) B) C) D) 8) 9) cos (60 ) A) B) C) D) 9) 0) sin 5π 0) A) - B) - C) D) ) cos 5π 4 ) A) - B) C) - D)
4 ) sin (-60 ) ) A) - B) - C) D) ) cos (5 ) ) A) B) - C) - D) - Use su calculadora para encontrar el valor de la funcción a cuatro lugares decimales. 4) sin (4 50') A) B) C) D) ) 5) cos (86 ) A) B) C) D) ) 6) sin (. ) A) 0.97 B) 0.00 C) D) ) 7) sin(.57) A) B) 0.7 C) 0.96 D) 0 7) 8) cos(-5π/8) A) B) 0.99 C) D) ) Encuentre la amplitud o periodo según se indique. 9) Encuentre la amplitud de = - sin + π 4. 9) A) B) C) π 4 D) -6 40) Encuentre el periodo de = - sin 4 + π. 40) A) π B) C)4 D) π 4) Encuentre la amplitud de = - cos ( - π). A) B) π C) -6 D) 4) Encuentre el desface de la funcción. 4) = sin - π 4) A) π 4 B) -π C) π D) π 4
5 4) = sin + π 4 4) A) π 4 B) π C) - π 4 D) -π Identifique cuál de las siguientes mejor representa la gráfica de la funcción trigonométrica dada: 44) f() = sin () 44) -π -π π π A) B) -π -π π π - -π -π π π C) D) -π -π π π - -π -π π π
6 45) f() = sin 45) -π -π π π A) B) -π -π π π - -π -π π π C) D) -π -π π π - -π -π π π
7 Find the eact values of the indicated trigonometric functions. Write fractions in lowest terms. 46) 46) Find sin A and cos A. A) sin A = 4 ; cos A = 4 B) sin A = 5 4 ; cos A = 5 C)sin A = 5 ; cos A = 4 5 D) sin A = 4 5 ; cos A = 5 47) 47) Find tan A and cot A. A) tan A = 5 ; cot A = 5 C)tan A = 5 ; cot A = B) tan A = 5 ; cot A = 5 D) tan A = ; cot A = 5 48) 5 48) 7 8 Find sec A and csc A. A) sec A = 5 8 ; csc A = 8 5 C)sec A = 8 5 ; csc A = 7 7 B) sec A = 7 7 ; csc A = 5 8 D) sec A = 7 7 ; csc A = 8 5 7
8 Solve the right triangle. 49) A = 6 7', a = 8.67 A) B = 7 ', b = 7.5, c = 9.7 B) B = 6 7', b = 7.5, c =.9 C)B = 6 ', b = 4., c = 9.7 D) B = 6 ', b = 4., c = ) 50) a = 6.6, b =.8 A) A = 7., B = 5.7, c = 7.4 B) A = 5.7, B = 7., c = 7.4 C)A = 40.4, B = 49.6, c = 4. D) A = 7., B = 5.7, c = 4. 50) 5) a = 9.5, c = 7. A) A = 45.8, B = 45.8, b = 9 B) A = 45.8, B = 44., b =.5 C)A = 54.4, B = 5.6, b =.5 D) A = 45.8, B = 44., b = 9 5) Solve triangle, if possible. If necessar, round our answers to the nearest tenth. 5) 5) 0 a b A) C = 0, a 6, b 9 B) C = 0, a 44.4, b 5. C)C = 97, a 8.8, b 5.7 D) C = 0, a 9, b 6 5) 5) c 8. b A) B = 7., b 6.9, c 56. B) B = 7., b 6.4, c.5 C)B = 6.8, b 5.8, c 6.9 D) B = 7., b 56., c 6.9 8
9 54) 54) 5 50 B 7 A) b 6.4, A 45., C 84.7 B) b 5.4, A 84.7, C 45. C)b 4.4, A 84.7, C 45. D) b 5.4, A 45., C ) C ) A) c 7, A.8, B 8. B) c 8, A.8, B 8. C)c 6, A 8., B.8 D) c 7, A 8., B.8 Multipl and simplif. 56) (cos - sin ) A) cos + sin B) cos + sin - sin C) D) - sin cos 56) 57) cot (sin - sec ) A) cot + csc B) tan - sin C)cos - csc D) cos - cot 57) 58) sec (cot + sin ) A) csc + tan B) cos + sin C)cos - cot D) sin + csc 58) 59) (sin - cos )(sec + csc ) A) cot + csc B) tan - cot C)cos - cot D) tan - sin 59) 60) ( + cot θ) A) csc θ + cot θ B) cos θ - cot θ C) + sin θ D) sin θ + csc θ 60) 6) ( - cot θ) A) sin θ + csc θ B) cos θ - cot θ C)csc θ - cot θ D) + sin θ 6) 6) ( - cos )( + cos ) A) sin B) + sin C)cos - D) sin + csc 6) Factor and simplif. 6) - sin + sin4 A) ( - sin ) B) ( + tan ) C)cos4 D) sin 6) 9
10 64) sec csc - 5 csc A) csc (sec - 5 csc ) B) sec (sec - 5 csc ) C)(csc - 5)(sec + csc ) D) csc (sec - 5 csc ) 64) 65) sec4 - sec tan + tan4 A) B) C)sec ( + tan ) D) sec + tan 65) 66) sin + sin cot A) B) cot + C)sin + D) cot - 66) 67) tan4 - sec4 A) - tan - B) sec C)sec + tan D) tan - sec 67) 68) sin4 - cos4 + cos A) cos B) 0 C) D) sin 68) 69) 8 cos + 6 cos + 8 A) 8 sin (cos + 8) B) (8 cos + )(cos + 8) C)8 sin D) 8(cos + ) 69) Simplif the epression. 70) - sin sin - csc 70) A) sin B) cos C) -cos D) -sin 7) 5 cos sin 5 sin cos 7) A) cos tan B) cos cot C) sin cot D) cos cot Find the eact value in radians. 7) cos- 7) A) π 4 B) π 6 C) π 6 D) 7π 4 7) tan- (-) 7) A) 5π 4 B) π 4 C) 7π 4 D) π 4 74) sin- (0.5) A) - π B) π C) π 6 D) - π 6 74) 0
11 75) sec- (-) 75) A) π B) π C)0 D) π Find the eact value in degrees. 76) sin- A) 45 B) 60 C) 5 D) 0 76) 77) cos- A) 45 B) 0 C) 5 D) 0 77) 78) sin- (0.5) A) 40 B) 60 C) 0 D) -0 78) 79) cot- A) 60 B) 0 C) -0 D) 45 79) Use a calculator to find the value of the function in degrees, rounded to the nearest hundredth of a degree. 80) sin A) 45.7 B) C) 5.7 D) ) 8) cos- (-0.78) A) -6.6 B) 5.55 C) 06.6 D) 6.6 8) 8) tan A) 8.7 B) -5.4 C) 5.4 D) 4. 8) 8) sin- (-0.404) A).0 B) -.85 C).85 D).85 8) Give the value of the function in radians. Round our answer to three decimal places. 84) sin A).96 B).777 C) D) ) 85) cos- 0.0 A) 4.50 B) 0.0 C).68 D) ) 86) tan-.544 A) 4.7 B) C) D).46 86) 87) cot A).4 B) C) 4.04 D) )
12 Solve, finding all solutions. 88) sin = (Epress our answer in radians.) 88) A) π 6 + kπ and - π 6 + kπ, where k is an integer B) π + kπ, where k is an integer C) π 6 + kπ and 5π 6 + kπ, where k is an integer D) π + kπ and π + kπ, where k is an integer 89) cos = - (Epress our answer in radians.) 89) A) π 6 + kπ and - π 6 + kπ, where k is an integer B) π 6 + kπ and 5π 6 + kπ, where k is an integer C) π + kπ and π + kπ, where k is an integer D) π + kπ and 4π + kπ, where k is an integer 90) tan = - (Epress our answer in radians.) 90) A) π 4 + kπ and 7π 4 + kπ, where k is an integer B) π + kπ and π + kπ, where k is an integer C) π 4 + kπ and 5π 4 + kπ, where k is an integer D) kπ and π + kπ, where k is an integer 9) sin = - (Epress our answer in degrees.) A) 5 + k 60 and 5 + k 60, where k is an integer B) 40 + k 60 and 00 + k 60, where k is an integer C)5 + k 60 and 5 + k 60, where k is an integer D) 45 + k 60 and 5 + k 60, where k is an integer 9) 9) cos = - (Epress our answer in degrees.) A) k 60 and 80 + k 60, where k is an integer B) 80 + k 60, where k is an integer C)k 60, where k is an integer D) 90 + k 60 and 70 + k 60, where k is an integer 9)
13 9) sin = - (Epress our answer in degrees.) A) 70 + k 60, where k is an integer B) k 60 and 80 + k 60, where k is an integer C)90 + k 60, where k is an integer D) 90 + k 60 and 70 + k 60, where k is an integer 9) Solve, finding all solutions in [0, π). 94) 4 cos + = 4.68 A) 0.646,.756 B) 0.646,.854 C) 0.956,.854 D) 0.646, ) 95) tan = A).85 B).85, 5.68 C) ,.85 D).85, ) 96) 4.8 cos +.4 = 0 A) π 6, 7π 6 B) π, 4π C) 5π 6, 7π 6 D) 5π 6, π 6 96) 97) 7 tan - = 0 A) π, 4π B) 5π 6, 7π 6 C) 5π 6, π 6 D) π 6, 7π 6 97) 98).5 csc = 0 A) ,.970 B).970, C) , D) 0.785, ) 99) sin + =.56 A) 0.904,.40 B) 0.904,.8 C) ,.40 D) , ) 00) 4.8 sin -.4 = 0 00) A) π 6, 7π 6 B) π 6, 5π 6 C) π, 5π D) π, π
14 Answer Ke Testname: MATE7_PRACTICA_FINAL ) B ) D ) A 4) C 5) D 6) A 7) D 8) C 9) C 0) A ) C ) B ) C 4) C 5) C 6) D 7) A 8) D 9) C 0) D ) C ) B ) D 4) D 5) D 6) D 7) A 8) B 9) D 0) A ) C ) B ) A 4) D 5) A 6) B 7) A 8) B 9) B 40) D 4) D 4) A 4) C 44) C 45) B 46) D 47) A 48) D 49) C 50) A 4
15 Answer Ke Testname: MATE7_PRACTICA_FINAL 5) D 5) D 5) D 54) D 55) A 56) D 57) C 58) A 59) B 60) A 6) C 6) A 6) C 64) A 65) B 66) A 67) A 68) D 69) D 70) D 7) B 7) A 7) D 74) C 75) A 76) B 77) A 78) C 79) B 80) A 8) C 8) A 8) B 84) C 85) C 86) B 87) D 88) D 89) D 90) A 9) A 9) B 9) A 94) D 95) B 96) C 97) D 98) D 99) A 00) D 5
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