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“NOCIONES BÁSICAS DE TRIGONOMETRÍA”
FUNCIONES BÁSICAS DE TRIGONOMETRÍA
“COORDENADAS POLARES”

DOCENTE DEL CURSO :
MG. JUAN BARDALES MÍO

Pimentel, 2005

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En los problemas del 1 al 6, determinar las funciones dadas.

a + b = c b + a + b = 90º
b + c = 90º 2b + a = 90º
cos (2b) = cos (90º – a)
= sen a

45. Si: [pic], calcular
x2 + 4k2 = 100
x2 + 25k2 = 289
21k2 = 189
k2= 9
k = 3
x2 + 36 = 100
x = 8
tan ( = [pic]

46.
[pic]
[pic]

[pic] [pic]
tan2 ( = 1/2
tan ( = 1/[pic] tan ( = [pic]
47. ( k = [pic] sen ( = [pic] sen B
k = [pic] (sen ( – sen B)

48.

BC ₧ 2 R sen (

49.
tan ( = ??

3 sen ( – cos ( = 3
3 sen ( – 3 = cos (
9 (sen ( –1)2 = cos2 (
9 (sen2( –2 sen ( + 1) = 1 – sen2(
10 sen2( – 18 sen ( + 8 = 0
5 sen2( – 9 sen ( + 4 = 0
5 sen ( –4 = – 4 sen (
sen ( –1 = – 5 sen (
– 4 sen (
sen ( = 4/5 sen ( = 1
( = 53º ( = 90º

I Caso
tan ( = [pic]

II Caso

tan ( = [pic]

50.Área = [pic]
Área = (B2 – b2) tan (
51.

tan A = [pic]
2 tan A = tan (

52.

53.

tan (45º – () = [pic] 2 – 2 tan ( = 1 + tan (
[pic] 1 = 3 tan (
[pic] tan ( = 1/3
cot ( = 3

54. Si sen ( = [pic]

[pic]
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55. AB2 + BD2 = 169
16k2 + (BC2 +CD2) = 169
16k2 + 9k2 + 144 = 169
25k2 = 25
k = 1

ctg ( = csc (
= [pic]
[pic] ctg ( – csc ( = 4 – 13/4
= 3/4

57

tan ( = [pic]

PRÁCTICA Nº 3

1. P (x , [pic])

P (–4, 4[pic])

2. P (–4 , [pic])

P (–4, [pic])
P(2, –2[pic])
3. (1, –[pic])

P (1, – [pic])
P ([pic])

4.

(–2, –2[pic])
(4, [pic])

5.

(–[pic])
(2, [pic])

6. y4 = x2 (a2 – y2)
[r sen (]4 = [r cos (]2 [a2 – r2 sen2 (]
r4 sen4( = r2 cos2( (a2 – r2 sen2 ()
r2 sen4( = cos2( (a2 – r2 sen2 ()
r2 sen4( = a2 cos2( – r2sen2( cos2(
r2 [sen4( + sen2( cos2(] = a2 cos2(
r2 sen2([sen2( + cos2(] = a2 cos2 (
r2 sen2( = a cos2 (
r2 = [pic]
r2 = a cot2 (

7. (x2 + y2)2 = (x2 – y2)2
[r2]3 = [r2 cos2( – r2 sen2(]2
r6 = [r2 (cos2( – sen2()]2
r6 = r4 (cos 2 ()2
r2 = cos2 (2()
r = cos (2()

8. (x2 + y2)2 + 2ª x (x2 + y2) – a2 y2 = 0
(r2)2 + 2ª r cos ( (r2) – a2 r2 sen2 ( = 0
r4 + 2ar2 cos( – a2r2 sen2 ( = 0r2 + 2ar cos( – a2 sen2( = 0
r2 + 2acos(r + a2cos2( = a2 sen2( + a2 cos2(
(r + acos()2 = a2(sen2( + cos2()
(r + acos()2 = a2 r = –a cos( ( a
r + a cós ( = ( a r = a (–cos( ( 1)
r = a (1 – cos2()
r = –a (1 + cos()
9. r (1 – 2 cos () = 2
r – 2r cos ( = 2
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x2 + y2 = 4 + 8x + 4x2
0 = 3x2 – y2 + 8x + 410. r = a sem 3 (
r2 = ar [sen (2( + ()]
r2 = ar [sen 2( cós ( + sen ( cos 2 (]
r2 = ar [2 sen ( cos2( + sen ( (r – 2 sen2()]
r2 = ar [2 sen ( (r – sen2() r sen ( – 2 sen3(]
r2 = ar [3 sen ( – 4 sen3(]
r2 = ar sen ( [3 – 4 sen2 (]
r2 = ar sen ( [3r2 – 4r2 sen2(]
(x2 + y2)2 = ay [3 (x2 + y2) – 4y2]
(x2 + y)2 = a [3x2y + 3y3 – 4y3]
(x2 + y2)2 = a...
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