τριγωνομετρικοί αριθμοί παραπληρωματικών γωνιών
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Transcript of τριγωνομετρικοί αριθμοί παραπληρωματικών γωνιών
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2.2 491
2.2
, 1800-
( 1800 )=
8
6
4
2
-2
-4
-10 -5 5
180-
(x,y)
( 1800 ) = ( 1800 ) =
A 00 1800, .
1. (), (),
) 1500 = 300 ) 1350 = 450
) 1000 = 800 ) 750 = 1050 ) 1100= 700 ) 1400= 400
) 1500 = (1800-1500)= 300 , (). ) 1350=- (1800-1350)= - 450 , (). ) 1000= -(1800-1000)= - 800, (). ) 750= -(1800-750)= - 1050, (). ) 1100=- (1800-1100)= - 700 , (). ) 1400 = (1800-1400)= 400 , ().
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2.2 492
2. x 0 x 1800, .
) x =600, x = ) x= 200, x = ... ) x = 300, x = ) 0 x 180 x = 600 x = 1200 ) x = 200= (1800 1600) =1600 - x =1600 ) x = 30 0 = (1800 1500) = 1500 x =1500
3. - .
. 1400 . 1400 . 1400
1. 400 2. 400 3. 400 4. 400 5. 400 6. 400
. 1 . 5 . 6
- ) 1200 ) 1350 ) 1500
1
) 1200 = (1800 600) = 600 = 23 , 1200 =
(1800600) = 600 = 21 , 1200 = (1800600) = 600 = 3
) 1350 = (1800 450)=450 =22 , 1350 = (1800450) =
=450 = 22 , 1350 = (1800 450) = 450 = 1
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2.2 493
) 1500 = (1800 300) = 300 = 21 , 1500 = (1800300) =
= 300 = 23 , 1500 = (1800 300) = 300 =
33
) 1080 + 770 720 + 1030 = 0 ) 1220 580 = 0 0135
2
) 1080 1030 : 1080 + 770 720 + 1030 = (1800 720) + 770 720 + (1800 770) = 720 + 770 720 770 = 0 ) 1220 1350 : 1220 580 = (1800 580) 580(1800 450) = 0135= 58 580 (1) = 58 + 580 = 0 3 ) 2 450 + 21350 = 1 ) 2 300 + 2600+ 2 1200 + 2 1500 = 2
) 1350 - : 2 45 0 + 2 135 0 = = 2 45 0 + 2 (180 0 450) = 2 45 0 + ( 450)2 = = 2 45 0 + 2 45 0 =2 2 45 0 = 2 1
44
422
22
2
===
) 1200 1500 2 300 + 2 60 0 + 2 1200 + 2 150 0 = =2 30 0 + 2 60 0 + 2 (180 0600) + 2 (180 0 300) = =2300 + 2602 +2600 + 2300 =22300 + 22600 = =22300 + 22300 = 2(2300 + 2300) = 21 = 2.
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2.2 494 (1400 + x )= (400 x ) (1580x ) = (220 + x )
4
(1400 +x ) +(400 x) = 1400 +x +400 x =1800 (1400 +x) = [1800 (400 x)] = (400 x) . (1580 x) + (220 +x) = 1580 x + 220 +x = 1800 (158 0 x ) = [1800 (220 + x)] = (220 + x) . 5
x ,
) x = 22 ) x = 1 x ) x =
23
) x = 21 ) x = 3 ) 2x = 1 + x
) x = 22 x = 450 x = 1800 450 = 1350
) x = 1 x x +x = 1 2x = 1 x = 21 ,
x = 300 x = 1500
) x = 23 x = 300
) x = 21 = 600 = (1800 1200) = 1200 -
x = 1200 . ) x = 3 = 600 = (18001200) = 1200 x = 1200. ) 2 x = 1 + x 2x x = 1 x = 1 x = 450 . -. ;
6
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2.2 495
- . .
= = 90 0.
) + + = 0 ) + = 0
7
3600
0360=+++ . -
. = , (1) = (2) .
000 3609090 =+++ 00 360180 =++ 000 180180360 ==+
) + + (1) (2) : + + = = + = 0 ) = : + = = 0 . - .
8
- . : ()2 = ()2 + ()2 = (6cm)2 + (8cm)2 ()2 = 36cm2 + 64cm2 =
100cm2 = 10cm. : =54
cm10cm8 ==
, =
53
cm10cm6 ==
, =
34
cm6cm8 ==
.
:
= 54= , = =
53 =
34
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2.2 496 6 cm , = 2 c m. N - - .
9
- . = = 3cm . = 2cm = = 1cm . . : ()2 + ()2 = ()2 ()2 + (3cm)2 = (6cm)2 ()2 + 9cm2 = 36cm2 ()2 = 36cm2 9cm2 = 27cm2 . = cm33cm39cm39cm27 2 === . : ()2 = ()2 + ()2 = (1cm)2 + 27cm2 = 1cm2 + 27cm2 = 28cm2 : = cm72cm74cm74cm28 2 === :
= 14
213772733
7233
cm72cm33 =
===
=14
7772
772
1cm72
cm1 ====
= 33cm1
cm33 == .
.
: = = 14
213 , = 14
7 , = 33
