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# 工職數學第一冊#6952

item11.

ans：C

1F
meimei Senior 32st (2015/02/02 23:01):

2F
asd49912037 primary 62st (2016/02/28 00:51):

item22.

ans：B

1F
meimei Senior 32st (2015/02/02 22:36):
B=4-7=-3

item33.

ans：D

note：數學
1F
meimei Senior 32st (2015/02/11 00:30):
cosA=cos(60度)=1/2=[(40^2)=(50^2)-(BC長)^2]/(2*40*50)

item44.

ans：D

1F
ChHautBrion Junior 32st (2014/10/18 18:06):

=> 0.5 = (41-x^2) / 40
=> x^2 = 21
=> x = 根號21(負不合)

item55.

ans：A

1F

=49+9-2*7*3*(1/2)
=37                         兩邊同時開根號
故 a=(37)^(1/2)

item66.

ans：C

1F
meimei Senior 32st (2015/02/12 14:08):
cosθ=( 52+ 72- 92)/2*5*7= -1/10......C

item77.

ans：D

1F
meimei Senior 32st (2015/02/05 23:03):
cosB=a^2+c^2-b^2)/2a*c=根號3/2

item88.

ans：B

1F
meimei Senior 32st (2015/02/02 23:21):
cosA=(6²+5²-7²)/2*6*5=1/5

item99.

ans：D

1F

cosA=(B^2+C^2-A^2)/2BC
a、b、c代入

item1010.

ans：D

1F

cosC=(A^2+B^2-C^2)/2AB

cosC=(4+6-4-2根號3)/4根號6

coC=(根號6-根號2)/4
C=75度

item1111.

ans：A

1F

cosA=(b^2+c^2-a^2)/2bc = (100+144-64)/(2*10*12)=3/4

item1212.

ans：C

1F

(AC)^2=7^2+6^2-2*7*6*(1/2)
=49+36-42
=43

(AC)=43^(1/2

item1313.

ans：B

1F

cosB=(4^2+5^2-6^2)/2*4*5
=(16+25-36)/40
=5/40
=1/8

item1414.

ans：D

1F
meimei Senior 32st (2015/02/03 11:14):
cosB=(8²+-7²)/2*8*5
=1/2

item1515.

ans：D

note：數學數學
1F

c^2=a^2+b^2-2abcosC
=4+9-6
=7
c=7^(1/2

item1616.

ans：A

note：數學
1F
meimei Senior 32st (2015/02/02 22:55):

item1717.

ans：D

1F
Ken Huang Junior 31st (2015/05/05 20:27):
gsesetg

item1818.

ans：B

1F
meimei Senior 32st (2015/02/02 22:15):

(式一*2)+式二得5a=3b,所以a:b=3:5

cosA=(5²+7²-3²)/2*5*7=13/14
sinA=√￣1-(13/14)²=3√￣3/14

item1919.

ans：B

1F
meimei Senior 32st (2015/02/13 19:04):

item2020.

ans：C

1F
meimei Senior 32st (2015/02/03 19:35):
cosC=(7^2+8^2-13^2)/2*7*8=-1/2

item2121.

ans：D

1F

=1/2*4*5*根號3/2

item2222.

ans：A

note：數學
1F
meimei Senior 32st (2015/02/03 19:38):
s=(3+5+6)/2=7

=2√14

item2323.

ans：D

1F
Ken Huang Junior 31st (2015/05/12 21:44):
XD

item2424.

ans：A

1F
Mirrow Chen Senior 12st (2013/05/03 22:08):
1/2 *8 *10*sin30

item2525.

ans：C

1F
Mirrow Chen Senior 12st (2013/05/03 22:09):
1/2*7*6*sin60

item2626.

ans：A

1F
Mirrow Chen Senior 12st (2013/05/03 22:16):
1/2*3*4*sin60
=6*^3/2
=3^3

item2727.

ans：D

note：數學
 best ans! 廖啟翔 Junior 21st (2012/02/14 15:20): 此題目 如能畫圖容易計算 (1)先畫出   2:1:根號3  的特殊三角形 (2) 再延伸根號.....看完整詳解

item2828.

ans：D

1F
meimei Senior 32st (2015/02/11 15:14):

item2929.

ans：C

1F
Chenjing Liao primary 22st (2011/12/21 19:28):

2F

3F
bvfjhthytfhv primary 12st (2014/06/25 16:39):

item3030.

ans：B

1F

= (2,-5)

item3131.

ans：D

1F
meimei Senior 32st (2015/02/03 09:47):

=1+3
=2

item3232.

ans：E

1F

item3333.

ans：D

1F

D( -1+5-2 , 1+0-(-3) )=( 2 , 4 )

item3434.

ans：D

note：數學
1F
Tina Shih Junior 21st (2014/11/26 12:35):
AB=CD,所以AB的平方=CD的平方,(6+1)平方+(8-5)的平方=49+9=58

item3535.

ans：B

note：數學
1F
anni105 Senior 21st (2015/01/10 18:04):

item3636.

ans：D

1F

a-2b=(2-2*3,1-(2*-4)
=(2-6,1-(-8))
=(-4,9)

item3737.

ans：A

1F
smartboqu Junior 22st (2014/03/19 10:25):

item3838.

ans：B

7F
Chris Wang Senior 21st (2012/12/30 11:07):

8F
Chris Wang Senior 21st (2012/12/30 11:13):

9F
Wen Zung Min kindergarten2st (2013/02/28 03:09):
OA係數應該也是T.用答案倒推的話.其實將4個答案代入即可找出能選的選擇.只是本末倒置

item3939.

ans：D

1F

k=-6

item4040.

ans：A

1F
meimei Senior 32st (2015/02/22 12:45):
u向量.v向量=|u向量||v向量|cos(夾角)

item4141.

ans：C

1F
anni105 Senior 21st (2015/01/10 18:05):

item4242.

ans：C

1F
meimei Senior 32st (2015/02/11 10:39):

item4343.

ans：B

1F
meimei Senior 32st (2015/02/03 09:43):

=4*5*[(4²+-)/2*4*5]
=-4

item4444.

ans：B

note：數學
1F
meimei Senior 32st (2015/02/11 09:48):

item4545.

ans：A

1F
meimei Senior 32st (2015/02/11 00:08):

| -3   -2  |

item4646.

ans：C

1F
ChHautBrion Junior 32st (2014/10/20 12:02):

| -1     3 |
|     X    |  =  -12
| 2      6 |
| -12 | = 12

item4747.

ans：A

1F
meimei Senior 32st (2015/02/11 00:16):

=[(-2+18)/40].(2,6)
=2/5(2,6)
=(4/5, 12/5)......A

item4848.

ans：B

1F
meimei Senior 32st (2015/02/03 19:52):
a向量*b向量=3*4cos30度=12*(3/2)=63

item4949.

ans：B

1F
appleeye Senior 31st (2014/04/03 22:25):

-20+15=-5

item5050.

ans：B

note：數學
1F

向量a．向量b = 5*(-1)+k*4=0
4k=5
k=5/4

item5151.

ans：C

1F
smile tower primary 11st (2015/01/31 21:01):

4:-3=-8:k

4k=24

k=6

item5252.

ans：D

note：數學
1F
meimei Senior 32st (2015/02/03 11:03):
a向量*b向量=3*6*cos120度
=3*6*(-1/2)
=-9

item5353.

ans：A

1F
meimei Senior 32st (2015/02/02 23:08):

3x/48=-1
3x=-48
x=-16  選(A)

item5454.

ans：D

1F

2y=-12
y=-6

item5555.

ans：D

note：數學
1F
meimei Senior 32st (2015/02/02 23:44):

item5656.

ans：A

1F
meimei Senior 32st (2015/02/03 18:37):

(3²+4²):[(8-3)²+(-8-4)²]  =線段OC:線段CB
=5:13

item5757.

ans：C

note：數學數學
1F

item5858.

ans：D

1F
ChHautBrion Junior 32st (2014/10/18 17:58):

|-8| = 8

item5959.

ans：C

1F

=(3,2)

item6060.

ans：A

1F
Luzette Junior 22st (2014/10/31 18:32):

A,B中點為(3-5)/2,(-2+6)/2=(-1,2)

item6161.

ans：B

1F

item6262.

ans：C

1F

2F

3F
asd49912037 primary 62st (2016/02/28 00:52):

item6363.

ans：B

1F

=(1+4) ^ (1/2)
=5^(1/2)

item6464.

ans：D

1F
meimei Senior 32st (2015/02/03 18:55):
p( (3-1)/2 , (-4)/2 )=(1,-2)
p與原點距離=√[(1)^2+(-2)^2=√5

item6565.

ans：C

1F
Luzette Junior 22st (2014/10/31 18:28):
f(x)=-8(常數)，因此-8+(-8)+(-8)=-24

item6666.

ans：A

1F
meimei Senior 32st (2015/02/02 23:18):

item6767.

ans：C

1F

A：460/360 餘數為100 故在第二象限
B：800/360 餘數為80 故在第一象限
C：950/360 餘數為230 故在第三象限
D：370/360 餘數為10 故在第一象限

item6868.

ans：E

1F

10*10*(75/360)*π
=(125/6)π

item6969.

ans：D

1F
ChHautBrion Junior 32st (2014/10/18 18:03):
tanθ + cotθ = sinθ/cosθ + cosθ/sinθ = [ (sinθ)^2+(cosθ)^2 ]/sinθcosθ = 1/sinθcosθ

item7070.

ans：A

note：數學
1F
meimei Senior 32st (2015/02/03 20:13):
tan70(>1)>°sin70°>cos70°

item7171.

ans：B

1F
meimei Senior 32st (2015/02/22 12:34):

=1+cotA-cscA+tanA+1-secA+secA+cscA-secAcscA
=2+cotA+tanA-sceAcscA
=2......B

item7272.

ans：D

1F
meimei Senior 32st (2015/02/22 11:16):

item7373.

ans：B

1F
meimei Senior 32st (2015/02/03 19:16):

=19/12

item7474.

ans：C

1F

cos θ =5/13
sin θ =12/13
tan θ =sin θ /  cos θ =12/5
cot θ =1 / tan θ =5/12
sec θ =1 / cos θ =13/5
csc θ =1 / sin θ =13/12

item7575.

ans：D

note：數學
2F
meimei Senior 32st (2015/02/02 21:57):
(A)改成sin²θ+cos²θ=1
(B)改成sec²θ-1=tan²θ
(C)改成1-sin²θ=1/sec²θ
(E)改成1+cot²θ=csc²θ

item7676.

ans：C

note：數學數學
1F
Mirrow Chen Senior 12st (2013/05/03 22:14):

sin=3/^10  cos=1/^10

item7777.

ans：D

1F
meimei Senior 32st (2015/02/11 09:25):
p=cosΘ+sin(π/2+Θ)+cos[(3π/2)+Θ]+sin[(3π/2)+Θ]
=cosΘ+sin(Θ)-cosΘ-sin(Θ)=0......D

item7878.

ans：A

1F
meimei Senior 32st (2015/02/11 09:13):

=1-1=0......A

item7979.

ans：B

1F
meimei Senior 32st (2015/02/03 10:34):

=(1/2)+(-1/2)-(-1)=1

item8080.

ans：D

note：數學
1F

sin(-15)=sin(30-45)=sin30cos45-cos30sin45=(1/2)*(√2/2)-(√3/2)*(√2/2)=√2/4-√6/4=(√2-√6)/4

item8181.

ans：A

1F
meimei Senior 32st (2015/02/03 19:11):
cotθ=-3

item8282.

ans：B

note：數學
1F
meimei Senior 32st (2015/02/03 14:02):
a=cos675°=cos(720°-675°)=cos45°=√2/2
b=sin120°=sin60°=√3/2
c=sin(-330°)=sin(-330°+360°)=sin30°=1/2

(B)(c)b>a>c
(D)a,b為無理數.c為有理數
2F

item8383.

ans：D

note：數學
1F
meimei Senior 32st (2015/02/03 18:45):
cot20π/3=cot2π/3=-cotπ/3=-√3/3

item8484.

ans：A

1F
Blake Huang (2012/07/11 18:26):
-1+(-0,5)+(-0.5)=2

2F

item8585.

ans：D

note：數學
1F
meimei Senior 32st (2015/02/03 09:58):

=sin30°-cos60°+tan45°
=(1/2)-(1/2)+1
=1

item8686.

ans：E

1F
meimei Senior 32st (2015/02/11 00:34):

item8787.

ans：D

1F
meimei Senior 32st (2015/02/03 19:44):
sin310°=-sin(360°-310°)=-sin50° =-cos40°=cos(40°+180°)=cos220°
=-sin(310°-180°)=-sin130°

item8888.

ans：B

note：數學
1F

= cos(105°+θ+135°-θ)
= cos(240°)
= -cos60°
= -(1/2)

item8989.

ans：C

note：數學
1F
meimei Senior 32st (2015/02/03 10:08):
sin(α-β)=sinα*cosβ-cosα*sinβ
=(4/5)*(5/13)-(-3/5)*(-12/13)
=(20/65)-(36/65)
=(-16)/65
選C

item9090.

ans：C

1F
meimei Senior 32st (2015/02/05 23:47):

=tan(20度+25度)*[1-tan(20度)*tan(25度)]+tan(20度)*tan(25度)
=tan(45度)*[1-tan(20度)*tan(25度)]+tan(20度)*tan(25度)
=1

item9191.

ans：C

1F

f(x)=cos^2(2x)-cos(2x)+1=(cos2X-1/2)^2+3/4

2F

item9292.

ans：D

note：數學
 best ans! Ming Hui Junior 32st (2012/04/01 16:55): 答案應該.....看完整詳解
2F

item9393.

ans：C

1F

(sinθ+cosθ)^2=(sinθ)^2+(cosθ)^2+2sinθcosθ-1
=1+sin2θ-1
=sin2θ

item9494.

ans：B

1F
ChHautBrion Junior 32st (2014/10/18 18:00):
(sin15 + cos15)^2 = (sin15)^2 + (cos15)^2 + 2cos15sin15 = 1 + sin2*15
= 1 + sin30 = 1.5

item9595.

ans：B

1F

cos(a-b)=cosa*cosb+sina*sinb
=(3/5)*(5/13)+(4/5)*(12/13)
=63/65

item9696.

ans：B

note：數學
1F

cos(240+θ)cos(60+θ)+sin(240+θ)sin(60+θ)
=cos(240+θ-60-θ)
=cos(180)
=-1

item9797.

ans：C

1F
meimei Senior 32st (2015/02/11 00:39):

c+a=5r......(2)
a+b=6r......(3)
[(1)+(2)+(3)]/2得a+b+c=15r/2

item9898.

ans：B

note：數學
1F
ChHautBrion Junior 32st (2014/11/01 09:06):

b            c                10        30
------  =  ------   =>    ------ = ------
sinB      sinC           sinB     sinC

item9999.
99.△ABC中，線段AC=8，角A=30度，角C=45度，則線段BC的邊長為
(A)2√2
(B)4√6-4√2
(C) 6√2
(D)8√2
(E)8

ans：B

1F

a/sin30°=8/sin105     又sin105°＝sin﹙60°＋45°﹚ ＝sin60°cos45°＋cos60°sin45° ＝﹙√3／2﹚﹙√2／2﹚＋﹙1／2﹚﹙√2／2﹚ ＝﹙√6／4﹚＋﹙√2／4﹚    且 sin30°=1/2
a=8/(﹙√6／4﹚＋﹙√2／4﹚)*(1/2)=4√6-4√2

item100100.

ans：D