C 5 Trigonometria

download C 5 Trigonometria

of 26

Transcript of C 5 Trigonometria

  • 7/23/2019 C 5 Trigonometria

    1/26

    :

    N .

    N

    .

    .

    , :

    ()

    () .

    OA

    5

  • 7/23/2019 C 5 Trigonometria

    2/26

    8 5:

    ,

    , 50 000 ,

    .

    .

    .

    ,

    .

    .

    1:

    150 . , 25%

    .

    , , ,

    24 /;

    . 6 / . 18 / . 25 /. 30 / . 49 /

    2:

    ,

    45

    150 , ;

    . 173 . 212 . 285 . 300

    by skysails

  • 7/23/2019 C 5 Trigonometria

    3/26

    9 5:

    3:

    ,

    0,42 ,

    .

    ,

    20%.

    2 500 000 .

    ;

    .

    :

    :

    :117

    :18

    :12 000

    :19

    : 3 500 000

  • 7/23/2019 C 5 Trigonometria

    4/26

    10 5:

    2 + 2 =2

    .

    :

    ( = 90) :

    .

    , , . :

    .

    ,

    =

    :

    12 10 .

    12 10 12 10 2

    2

    = .

    .

    =

    =

    =

    =++

    :

    :23

    =4

    2 6 = 3 4

    23

    =4

    =2+43+

  • 7/23/2019 C 5 Trigonometria

    5/26

    11 5:

    (1)

    .

    () .

    ,

    (y), .

    ,

    ()

    .

    C_En5_TrigArithmoi.ggb,

    .

    ,

    38.

    .

    , .

    27 5,444 2,774 6,11 0,454 0,891 0,5138

    38

    38

    38

    40

    40

    40

    40

    http://../C_APPLETS/C_En5_TrigArithmoi.ggbhttp://../C_APPLETS/C_En5_TrigArithmoi.ggbhttp://../C_APPLETS/C_En5_TrigArithmoi.ggbhttp://../C_APPLETS/C_En5_TrigArithmoi.ggbhttp://../C_APPLETS/C_En5_TrigArithmoi.ggbhttp://../C_APPLETS/C_En5_TrigArithmoi.ggbhttp://../C_APPLETS/C_En5_TrigArithmoi.ggb
  • 7/23/2019 C 5 Trigonometria

    6/26

    12 5:

    (2)

    . :

    ;

    .(

    C_En5_TrigArithmoi.ggb

    .)

    45

    ( ) .

    .

    , . ,

    .

    . , , , , .

    , (, , ). . 17 .. . .

    http://../C_APPLETS/C_En5_TrigArithmoi.ggbhttp://../C_APPLETS/C_En5_TrigArithmoi.ggbhttp://../C_APPLETS/C_En5_TrigArithmoi.ggbhttp://../C_APPLETS/C_En5_TrigArithmoi.ggb
  • 7/23/2019 C 5 Trigonometria

    7/26

    13 5:

    .

    .

    .

    B:

    .

    : .

    A:

    =

    =

    =

    =

    =

    =

    :

    :

    :

    -

    ,

    -

    .

  • 7/23/2019 C 5 Trigonometria

    8/26

    14 5:

    :

    , : =

    =

    1.

    .

    :

    ::

    :: : .

    :: .:

    =

    =

    =

    3

    =

    =

    =

    4

    =

    =

    =34

    =

    =

    =4

    =

    =

    =3

    =

    =

    =

    4

    3

    -

    .

    -

    ,

    DEG D.

  • 7/23/2019 C 5 Trigonometria

    9/26

    15 5:

    2. 45

    .

    :

    45,

    = = 1 .

    .

    ,()2 = ()2 + ()2

    ()2 = 12 + 12

    ()2 = 2

    =2

    =

    45 = 2

    =

    45 = 2

    =

    45 =

    45 = 1

    :

    2 2 :

    , 45 = 2

    = 2

    22=

    2

    2 =

    22

    45 =22

    3. 30 =2.

    30 60.

    :

    30 =2. , = 1 = 2

    .

    ,()2 = ()2 + ()2

    22 = 12 + ()2

    ()2 = 4 1

    ()2 = 3

    =3

    2

  • 7/23/2019 C 5 Trigonometria

    10/26

    16 5:

    :

    =

    30 =2

    =

    30 =32

    =

    30 = 3

    = 333

    30 =33

    60.

    =

    60 =32

    =

    60 =2

    = 60 =3 =3

    30, 45 60 :

    30 45 60

    2 2

    2

    32

    32

    22

    2

    33 1 3

    4. , ,

    :

    () 30 () 42 () 70

    :

    :

    30 300.5

    42 420.7431448255

    70 702.747477419

    . ,

    30 = 0,5 42 0,743 70 2,747

    0 =sin 3

    2cos 4 =

    tan 7 0 =

  • 7/23/2019 C 5 Trigonometria

    11/26

    17 5:

    5. ,

    , :() = 0,9 () = 0,5 () = 2,2

    :

    .

    . :

    = 0,9 0.9

    64.15806724

    = 0,5 0.5

    60

    = 2,2 2.2

    65.55604522

    . ,

    64 = 60 66

    1. .

    N .

    SHIFT

    SHIFT

    SHIFT

    =

    =

    =

    . 9sin 0

    tan 2 . 2

  • 7/23/2019 C 5 Trigonometria

    12/26

    18 5:

    2. =37;

    () () ()

    3. , :

    ()

    4;

    () 4

    ;

    4. . :

    () =3 :

    . =34 . =

    4 . =3

    4

    () = 3 =2

    3 :

    . = 2 . =2

    . =3

    () = 0,5 :

    . = 45 . = 30 . = 60

    () = 45 :

    . = .

    5.

    .

    ()

    =

    ()

    =

    () =

  • 7/23/2019 C 5 Trigonometria

    13/26

    19 5:

    6.

    . 3

    .

    () 75 () 78 () 60() 23 () 52 ()88

    7. .

    .

    () = 0,5 () = 0,3 () = 0,25

    () =32

    () = 3 () = 3,1

    8. :

    () 65 = () 50 =

    () 10 = () 34 = 56

    () =45 () =

    9. =

    3 = 1

    2

    3. , ,

    . ,

    .

    10.

    . ;

  • 7/23/2019 C 5 Trigonometria

    14/26

    20 5:

    11.

    :

    12. ( = 90) :

    () 0

  • 7/23/2019 C 5 Trigonometria

    15/26

    21 5:

    O

    , . ,

    .

    .

    C_En5_Dierevnisi_Paralia.ggb,

    .

    -

    .

    http://../C_APPLETS/C_En5_Dierevnisi_Paralia.ggbhttp://../C_APPLETS/C_En5_Dierevnisi_Paralia.ggbhttp://../C_APPLETS/C_En5_Dierevnisi_Paralia.ggbhttp://../C_APPLETS/C_En5_Dierevnisi_Paralia.ggbhttp://../C_APPLETS/C_En5_Dierevnisi_Paralia.ggbhttp://../C_APPLETS/C_En5_Dierevnisi_Paralia.ggbhttp://../C_APPLETS/C_En5_Dierevnisi_Paralia.ggbhttp://../C_APPLETS/C_En5_Dierevnisi_Paralia.ggb
  • 7/23/2019 C 5 Trigonometria

    16/26

    22 5:

    .

    .

    :

    40,

    10 .

    , ,

    (

    ).

    .

    ,

    ;

    ,

    ;

    60

    4

  • 7/23/2019 C 5 Trigonometria

    17/26

    23 5:

    .

    :

    ()

    :

    : = 90 = 53 = 180 (90 + 53) = 37

    =

    53 = 3

    0,6 3

    0,6 3

    3,

    5

    , = 3 = 4 = 5

    =

    53 =3

    1,33 3

    3 1,33

    3,99

    4

    :

    2 =2 +2 = 4

    () .

    :

    :

    2 =2 +2

    72 = 32 +2

    2 = 49 9

    =40

    6,3

    =

    =37

    0,43

    65

    , = 3 = 6,3 = 7

    = 90 = 65 = 180 (90 + 65) = 25

  • 7/23/2019 C 5 Trigonometria

    18/26

    24 5:

    1.

    . 6

    64.

    . (

    2 ).

    :

    64

    6. (), = 64. ,

    .

    =

    64 = 4

    4

    2,05 =

    = 2,05 6

    = 12,3

    64 2,05

    , 12,3 .

    2.

    , .

    :

    .

    .

    ,

    =

    =

    = 0,0 9

  • 7/23/2019 C 5 Trigonometria

    19/26

    25 5:

    . ,

    0.0909090909

    (5 55 )

    (0.09090909 ) 85. ,

    85.

    1. . .

    () ()

    () ()

    2. (2,1), (5,1)(5, 3).

    SHIFT

    SHIFT

    SHIFT

  • 7/23/2019 C 5 Trigonometria

    20/26

    26 5:

    3. (

    ):

    () ()

    () ()

    () ()

    4. :

    () 30, :

    i. 1 ,ii. 1 .

    () 45, :

    i. 1 ,ii. 1 .

    5. :

  • 7/23/2019 C 5 Trigonometria

    21/26

    27 5:

    6. , ,

    5 .

    7. , 8 , , .

    20,

    .

    8. .

    , .

    9. :

    10.

    6,40 . 12 ,

    30 .

    50 40 . ,

    75. 1,80 , .

  • 7/23/2019 C 5 Trigonometria

    22/26

    28 5:

    1. / , :

    () 1 =89 /

    () 30 =2 /

    () =4 =3

    4 /

    () = 45 = = /

    () 60 =20 /

    () 0

  • 7/23/2019 C 5 Trigonometria

    23/26

    29 5:

    4.

    30

    30.

    .

    5.

    ,

    25 0,42,25 0,91, 25 0,47.

    6. , = 90 , =2

    .

    7. = 2.

    8. :

    () ,

    .

    () , = 90, : =.

    9.

    , 4 . .

    10.

    .

    .

  • 7/23/2019 C 5 Trigonometria

    24/26

    30 5:

    11. ( = 90) :

    ++

    =

    12.

    .

  • 7/23/2019 C 5 Trigonometria

    25/26

    31 5:

    1. .

    .

    165 2 , .

    2. .

    .

    .

    3. 30

    60,

    (:

    1 ).

    4. :

    5. :

    =1

    2

    6. , :

    () 4 = 4 () 2 1 = 0

  • 7/23/2019 C 5 Trigonometria

    26/26

    7. . .

    8. . ,

    .

    .

    (),

    .

    ,

    -

    ,

    (),

    .

    .

    1

    . 90

    .

    .

    2

    .

    .

    .

    -

    .

    .

    -

    (.. -

    ).