01

CENTRO DE ESTUDIOS PREUNIVERSITARIOS ANTERO SOLANO Formando triunfadores

CIRCUNFERENCIA TRIGONOMTRICAProf. Antero Solano Lpez01.En la circunferencia trigonomtrica determinar MP.A) tg( + ctg(B) tg( ctg(C) ctg ( tg(D) (tg( + ctg()E) tg ( ctg(+102.En la circunferencia trigonomtrica mostrada. Halle el rea de la regin sombreada.

A)

B)

C)

D)

E)

03.En la circunferencia trigonomtrica de la figura mostrada, si AM = (; entonces al calcular (en u2) el rea sombreada, se obtiene:A)

B)

C)

D)

E)

04.En la circunferencia trigonomtrica mostrada P = (a, b) y mAQ = (. Halle .A)

B)

C)

D)

E)

05.Si (x, y ( R, determine la extensin de m para que la expresi+n dada sea vlida.A) 5 ( m ( 2

B) 2 ( m ( 5

C) m ( 5 ( m ( 2 D) m ( 2 ( m ( 5

E) 5 ( m ( 506.Si , determine los posibles valores para cos (.A)

B)

C)

D)

E)

07.En la figura M(x; y) es punto medio del segmento , ( = mABP. Halle x + y.A) (sen ( + cos()/2

B) 2 cos (C) 2 sen (D) sen (E) cos (08.Si |x| ( 4, entonces al calcular la suma del mximo y mnimo valor de la expresi+n , se obtiene:A) 1,5B) 2,5C) 3D) 3,5E) 4,509.Dadas las rectas y mostradas en la circunferencia trigonomtrica. Si mABP = ( y . Se pide determinar el rea de la regin triangular ONA.A)

B)

C)

D)

E)

10.En la figura mostrada la circunferencia es trigonomtrica, hallar el rea de la regin somrbeada (AP = ().A)

B)

C)

D)

E)

11.En la circunferencia trigonomtrica de la figura mostrada, determine el rea de la regin sombreada en trminos de (, siendo OP = PB. (mAM= ()A)

B)

C)

D)

E)

12.En la circunferencia trigonomtrica de la figura mostrada, si mABP = (, m(MOP=90, determine el rea de la regin trianfgular AMN (en u2).

A) 0,5 cot (() [cos (() 1]

B) 0,5 cot (() [sen (() 1]

C) 0,5 cot (() [1 sen (()]D) 0,5 tan (() [sen (() 1]

E) 0,5 tan (() [1 cos (()]13.Determine el rea de la regin sombreada en la circunferencia trigonomtrica mostrada. Si mABP = (.A) 0,5tan(() [1cos (]

B) 0,5cot(() [1cos (]

C) 0,5tan(() [1+cos (]D) 0,5cot(() [1+cos (]

E) 0,5tan(() [1+sen (]14.

A)B)C)

D)E)

15.

A)B)C)

D)E)

16.

A)B)C)

D)E)

17.

A)B)C)

D)E)

18.

A)B)C)

D)E)

19.

A)B)C)

D)E)

20.

A)B)C)

D)E)

21.

A)B)C)

D)E)

22.

A)B)C)

D)E)

23.

A)B)C)

D)E)

01.De la figura mostrada, halle:E = |a tg ( + d ctg (|

A) b + cB) b c C) c b D) (b + c)E) 002.En la figura AO = BO = 10u y la altura relativa a uno de los lados iguales mide 8u. Determinar: E = ctg ( ctg (A)

B)

C)

D)

E)

03.De la figura, hallar tg (A)

B)

C)

D)

A)B)C)

D)E)

E)

A)B)C)

D)E)

A)B)C)

D)E)

04.De la figura mostrada, calcule

M = tg ( + ctg (A)

B)

C)

D) 2E)

05.Del grfico mostrado halle:F = 25[sen (() + cos (()] + 24 tg (()

A) 38 B) 24 C) 21 D) 21E) 3806.De la figura mostrada, determine el valor de W en trminos de a, si:W = csc ( + sec (A)

B)

C)

D) aE) a 07.En el plano cartesiano XY, el segmento pasa por el origen de coordenadas; tal que A( 5; 1), adem+as . Si ( y ( son los ngulos indicados se pide hallar el valor de: E = tg ( ( tg (A) 1 B) 1C) 25 D) 25E)

08.Dada la figura: m = 2n Hallar csc (A)

B)

C)

D)

E)

09.De la figura halle el valor de:

A)

B)

C) 0D) 1 E) 110.Si sen ( = ( ( ( IIC, halle el valor de:

A)

B)

C)

D)

E) 111.Si y tg ( > 0, halle .A) 3B) 4C) 4D) 5E) 512.En la figura mostrada se tiene al ngulo ( en posicin normal. Calcule el valor numrico de:

A) 6 B) 6C) 12D) 18E) 2013.Del grfico mostrado, halle: S = sen( + tg (A)

B)

C)

D) 5/7E) 6/514.De la figura, si AM = MB, halle .A)

B)

C)

D)

E) 16115.De la figura mostrada, P = ( 16; 12). Halle: , paralelo al eje Y.A) 2B) 1C) 0D) 1 E) 2 16.De la figura mostrada, AO = OB; C = (9; 6) y G es el baricentro del tringulo ABC.Calcule:

A)

B)

C)

D)

E)

17.En la figura, halle el radio de la circunferencia con centro en B, en trminos de m y (.A)

B)

C)

D)

E)

18.En la figura mostrada las coordenadas del punto A son ( 2; 3). Calcule el valor numrico de:F = 6 tg (() 13 cos2 (()

A) 26 B) 13 C) 5 D) 5E) 1319.De la figura:A = (0; 4)B = (8; 5)

C = (7; 0))

G: Baricentro de la regin triangular ABC. Halle tg (().

A)

B)

C)

D)

E) 220.En la figura mostrada, AN = 3NB y las coordenadas del punto N son (a, 0). Si el valor del rea del tringulo OAB es a2, halle tg (().A)

B)

C)

D) 2/3E)

21.De la figura, si y halle un valor aproximado de tg (.A) 0,492B) 0,429C) 0,942D) 0,2246E) 0,29422.Dada la circunferencia, cuyo centro (P) se encuentra en el eje X. Si OA = 3HA, se le pide que determine tg (.A)

B)

C)

D)

E)

23.Dado el tringulo rectngulo ABC (recto en B); si: AC = 2AO, BC = 2CD y m(BDC = 90. Se pide determinar tg (.A)

B)

C)

D)

E)

24.En la figura mostrada OPQ es un tringulo rectngulo (recto en P) y M es punto medio. Determine:

A) 1B) 1 C) 2D) 2 E) 325.De la figura mostrada, halle ctg (, si .A)

B)

C)

D)

E) 126.Si ( es el ngulo que forman las rectas y del grfico mostrado entonces tan ( es igual a:A)

B)

C)

D)

E)

27.La figura muestra la interseccin de las rectas y

Determine el valor de tan (A) 4 B)

C)

D) 4E) 628.De la figura mostrada, calcule

A) 1 B)

C) 0D)

E) 429.De la figura mostrada, determine tan (, si .A)

B)

C) 1D) 2E) 430.Halle cot ( a partir de la figura mostrada, si M es punto medio de .A) 5B) 4C) 3D) 2E) 131.En la figura adjunta , pasa por el origen, si A( 1, 2), se le pide, que determine:

A) 2B) 3C) 4D) 5E) 632.En la figura mostrada, las coordenadas del punto A son (8; 3). Calcule el valor numrico de .A) 24 B) 16 C) 8 D) 8E) 1633.Con los datos de la figura mostrada determine:

A) 4 B) 2 C) 1 D)

E)

34.En la figura mostrada si: A = (5; 3), , calcule tan (().A) 5 B) 4 C) 3 D) 2 E) 1 35.De la figura mostrada si: P = (5; 4), calcule .A) 9

B) 8 C) 7D) 8E) 936.En la figura mostrada, C es el centro de la circunferencia de coordenadas ( 1; 3), adems OP y Q son puntos de tangencia, calcule: F = tan (|(|) tan (().A)

B)

C)

D)

E)

37.En la figura mostrada se cumple que: , m(QPA = 90; m(OAP = 18,5 y las coordenadas del punto P son ( 3; 6), Calcule E = tan (() + cot (()A)

B)

C)

D)

E)

38.En la figura mostrada, m(RPO = 53, m(QOT = 90, PQ = 2QR. Halle el valor de R = 8 tan (() 3 cot (()A) 5 B) 3C) 0D) 3E) 539.Si ( y ( son ngulos coterminales tal que y , halle .A)

B)

C)

D)

E)

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