高分悬赏:高中数学三角函数题! 高中数学三角函数题!
\u9ad8\u4e2d\u6570\u5b66\u4e09\u89d2\u51fd\u6570\u4efb\u610f\u89d2\u7684\u9898\u76ee\uff0c\u9ad8\u5206\u60ac\u8d4f\uff01\u5148\u6c42A\u2229B,\u6362\u4e2a\u5b57\u6bcd\uff0c\u5c06B\u4e2d\u7684k\u6362\u4e3am.
\u7531k*135=m*150,m=-10,-9,-8,...,8
\u53ef\u5f979k=10m,\u800c9\u548c10\u4e92\u8d28\uff0c\u6240\u4ee5m\u53ea\u80fd\u53d69\u7684\u500d\u6570\u7b49\u5f0f\u624d\u80fd\u6210\u7acb\u3002
\u4e5f\u5c31\u662fm=-9,0\u4e24\u4e2a\u6570\uff0c\u76f8\u5e94\u7684k=-10,0.
\u6240\u4ee5A\u2229B={-1350\u00b0\uff0c0\u00b0}
\u56e0\u6b64\u6240\u6c42\u7b54\u6848\u662f\uff1a
S={x|x=-1350\u00b0+n*360\u00b0\uff0cn\u662f\u6574\u6570}\u222a{x|x=n*360\u00b0\uff0cn\u662f\u6574\u6570}
\u6216\u8005\u5199\u6210S={x|x=-90\u00b0+n*360\u00b0,n\u662f\u6574\u6570}\u222a{x|x=n*360\u00b0\uff0cn\u662f\u6574\u6570}
1.w\u662f\u6b63\u5b9e\u6570\uff0c\u51fd\u6570f(x)=2sinwx\u5728[-\u03c0/3,\u03c0/4]\u4e0a\u662f\u589e\u51fd\u6570\uff0c\u6c42w\u53d6\u503c\u8303\u56f4\uff1a
\u7b54\u6848\uff1a0\uff1cw\u22643/2
sinx\u589e\u533a\u95f4\uff082k\u03c0-\u03c0/2\uff0c2k\u03c0+\u03c0/2\uff09
sinwx\u589e\u533a\u95f42k\u03c0-\u03c0/2<wx<2k\u03c0+\u03c0/2
\u533a\u95f4\u5305\u542b0
\u6240\u4ee5\u5e94\u8be5\u5728-\u03c0/2<wx<\u03c0/2
w>0
-\u03c0/2w<x<\u03c0/2w
\uff08-\u03c0/3,\u03c0/4]\u662f\u5b50\u533a\u95f4
\u6240\u4ee5-\u03c0/2w<=-\u03c0/3
1/2w>=1/3
w<=3/2
\u03c0/4<=\u03c0/2w
w<=2
0<w<=3/2
\u7b54\u6848\uff1a0\uff1cw\u22643/2
2.sin(\u03c0/2+a)+cos(\u03c0/2-a)=1/5a\u2208\uff080\uff0c\u03c0)\u6c42tana?
cos(a)+sin(a)=1/5
\u4e24\u8fb9\u5e73\u65b9\uff0c
1+2sinacosa=1/25,
sin2a=-24/25,
cos2a=(1-sin^2(2a))^0.5=\u00b17/25
cosa=\u00b1[(1\u00b1cos(2a))/2]^0.5
cosa=\u00b14/5,cosa=\u00b13/5
sina=\u00b13/5sin=\u00b14/5
a\u2208\uff080\uff0c\u03c0)
sina=3/5sina=4/5
cosa+sina=1/5
cosa=-3/5sina=4/5
tana=cosa/sina
\u7b54\u6848\uff1a-4/3
3.\u51fd\u6570y=sin(2x+\u03c0/6)-cos(2x+\u03c0/3)\u6700\u5c0f\u6b63\u5468\u671f\u548c\u6700\u5927\u503c\uff1f
y=sin(2x+\u03c0/6)-cos(2x+\u03c0/3)
=sin2x*(3^0.5/2)+cos2x*(1/2)-cos2x*(1/2)+sin2x*(3^0.5/2)
=3^0.5sin(2x)
\u6700\u5c0f\u6b63\u5468\u671fT=2\u03c0/2=\u03c0
\u6700\u5927\u503c\u662f\u221a3
\u7b54\u6848\uff1a\u03c0\u30011\uff08\u60f3\u8fd9\u79cd\u51fd\u6570\u5e94\u8be5\u600e\u4e48\u5904\u7406\uff1f\uff09
4\u30015\u03c0\uff1cA\uff1c6\u03c0\uff0ccosA/2=a,\u6c42sina/4?
sin(A/2)=\u00b1((1-cos(A/2)/2)^0.5
=\u00b1((1-a)/2)^0.5
5\u03c0\uff1cA\uff1c6\u03c0
5\u03c0/4\uff1cA/4\uff1c6\u03c0/4
sin(A/2)=-((1-a)/2)^0.5
-\u6839\u53f7\u4e0b1-a/2
5.\u2235\u68393sinx=-cos\u03b1
\u2234tan\u03b1=-\u68393/3
3^0.5sin\u03b1=-cos\u03b1
sin\u03b1/cos\u03b1=-3^0.5
tan\u03b1=sin\u03b1/cos\u03b1=-3^0.5
\u8fd9\u4e24\u90e8\u662f\u600e\u4e48\u56de\u4e8b\u554a\uff0c\u662f\u600e\u4e48\u5217\u51fatan\u03b1\u8fd9\u4e2a\u5f0f\u5b50\u7684\uff1f
6.cos\uff08\u03b1+\u03b2\uff09=1/3,cos(\u03b1-\u03b2\uff09=1/2\uff0c\u6c42log(5)tan\u03b1tan\u03b2=\uff1f
sins\u03b1in\u03b2=-1/2[cos(\u03b1+\u03b2)-cos(\u03b1-\u03b2)]=-1/2(1/3-1/2)=1/12
cos\u03b1cos\u03b2=1/2[cos(\u03b1+\u03b2)+cos(\u03b1-\u03b2)]=1/2(1/3+1/2)=5/12
log(5)tan\u03b1tan\u03b2=log(5)(sins\u03b1in\u03b2/cos\u03b1cos\u03b2)=log(5)(1/5)=-1
\u7b54\u6848\uff1a1/6
7.\u5df2\u77e5f(x)=2sin(\u03c0x/4+\u03c0/4)\uff0c\u6c42f(1)+f(2)+f(3)+....+f(2011)?
f(1)=2sin(\u03c0/4+\u03c0/4)=2
f(2)=2sin(2\u03c0/4+\u03c0/4)=2^0.4
f(3)=2sin(3\u03c0/4+\u03c0/4)=0
f(4)=2sin(4\u03c0/4+\u03c0/4)=-2^0.4
f(5)=2sin(5\u03c0/4+\u03c0/4)=-2
f(6)=2sin(6\u03c0/4+\u03c0/4)=-2^0.4
f(7)=2sin(7\u03c0/4+\u03c0/4)=0
f(8)=2sin(8\u03c0/4+\u03c0/4)=2^0.4
f(9)=2sin(9\u03c0/4+\u03c0/4)=2sin(2\u03c0+\u03c0/4+\u03c0/4)=2sin(\u03c0/4+\u03c0/4)2
\u2026\u2026
f(1)+f(2)+f(3)+....+f(8)=0
2011/8\u4f593
f(1)+f(2)+f(3)+....+f(2011)=2+2^0.5
\u7b54\u6848\uff1a2\u6839\u4e0b2+2
8.\u5224\u65ad\u5947\u5076\u6027\uff1a
f(x)=x²/sinx
g(x)=tanx+sinx
h(x)=lg(sinx+\u8ddf\u4e0b\uff081+sin²x\uff09)
f(-x)=(-x)^2/sin(-x)=-x²/sinx=-f(x)
g(-x)=tan(-x)+sin(-x)=-(tanx+sinx)=-g(x)
h(-x)=lg(sin(-x)+(1+sin²(-x)^0.5)=lg(-sinx+(1+sin²x)^0.5)=-h(x)
\u90fd\u662f\u5947\u51fd\u6570
\u7b54\u6848\uff1a\u90fd\u662f\u5947\u51fd\u6570
9.\u6247\u5f62\u5468\u957f6\uff0c\u9762\u79ef\u662f2\uff0c\u6c42\u6247\u5f62\u4e2d\u5fc3\u89d2\u7684\u5f27\u5ea6\u6570\uff1f
A*r=6A=6/r
3.14r^2=2r=(2/3.14)^0.5
A=6(2/3.14)^0.5
\u7b54\u6848\uff1a1\u62164
答案:0<w≤3/2
sinx增区间(2kπ-π/2,2kπ+π/2)
sinwx增区间2kπ-π/2<wx<2kπ+π/2
区间包含0
所以应该在-π/2<wx<π/2
w>0
-π/2w<x<π/2w
(-π/3,π/4]是子区间
所以-π/2w<=-π/3
1/2w>=1/3
w<=3/2
π/4<=π/2w
w<=2
0<w<=3/2
答案:0<w≤3/2
2.sin(π/2+a)+cos(π/2-a)=1/5a∈(0,π)求tana?
cos(a)+sin(a)=1/5
两边平方,
1+2sinacosa=1/25,
sin2a=-24/25,
cos2a=(1-sin^2(2a))^0.5=±7/25
cosa=±[(1±cos(2a))/2]^0.5
cosa=±4/5,cosa=±3/5
sina=±3/5sin=±4/5
a∈(0,π)
sina=3/5sina=4/5
cosa+sina=1/5
cosa=-3/5sina=4/5
tana=cosa/sina
答案:-4/3
3.函数y=sin(2x+π/6)-cos(2x+π/3)最小正周期和最大值?
y=sin(2x+π/6)-cos(2x+π/3)
=sin2x*(3^0.5/2)+cos2x*(1/2)-cos2x*(1/2)+sin2x*(3^0.5/2)
=3^0.5sin(2x)
最小正周期T=2π/2=π
最大值是√3
答案:π、1(想这种函数应该怎么处理?)
4、5π<A<6π,cosA/2=a,求sina/4?
sin(A/2)=±((1-cos(A/2)/2)^0.5
=±((1-a)/2)^0.5
5π<A<6π
5π/4<A/4<6π/4
sin(A/2)=-((1-a)/2)^0.5
-根号下1-a/2
5.∵根3sinx=-cosα
∴tanα=-根3/3
3^0.5sinα=-cosα
sinα/cosα=-3^0.5
tanα=sinα/cosα=-3^0.5
这两部是怎么回事啊,是怎么列出tanα这个式子的?
6.cos(α+β)=1/3,cos(α-β)=1/2,求log(5)tanαtanβ=?
sinsαinβ=-1/2[cos(α+β)-cos(α-β)]=-1/2(1/3-1/2)=1/12
cosαcosβ=1/2[cos(α+β)+cos(α-β)]=1/2(1/3+1/2)=5/12
log(5)tanαtanβ=log(5)(sinsαinβ/cosαcosβ)=log(5)(1/5)=-1
答案:1/6
7.已知f(x)=2sin(πx/4+π/4),求f(1)+f(2)+f(3)+....+f(2011)?
f(1)=2sin(π/4+π/4)=2
f(2)=2sin(2π/4+π/4)=2^0.4
f(3)=2sin(3π/4+π/4)=0
f(4)=2sin(4π/4+π/4)=-2^0.4
f(5)=2sin(5π/4+π/4)=-2
f(6)=2sin(6π/4+π/4)=-2^0.4
f(7)=2sin(7π/4+π/4)=0
f(8)=2sin(8π/4+π/4)=2^0.4
f(9)=2sin(9π/4+π/4)=2sin(2π+π/4+π/4)=2sin(π/4+π/4)2
……
f(1)+f(2)+f(3)+....+f(8)=0
2011/8余3
f(1)+f(2)+f(3)+....+f(2011)=2+2^0.5
答案:2根下2+2
8.判断奇偶性:
f(x)=x²/sinx
g(x)=tanx+sinx
h(x)=lg(sinx+跟下(1+sin²x))
f(-x)=(-x)^2/sin(-x)=-x²/sinx=-f(x)
g(-x)=tan(-x)+sin(-x)=-(tanx+sinx)=-g(x)
h(-x)=lg(sin(-x)+(1+sin²(-x)^0.5)=lg(-sinx+(1+sin²x)^0.5)=-h(x)
都是奇函数
答案:都是奇函数
9.扇形周长6,面积是2,求扇形中心角的弧度数?
A*r=6A=6/r
3.14r^2=2r=(2/3.14)^0.5
A=6(2/3.14)^0.5
答案:1或4
附加题:“根号下”怎么打符号?
^0.5
1.把 (wx) 作为一个整体来考虑,设u=wx
sin u 在 -π/2~π/2 范围内单调递增,则 -π/2<=u<=π/2
再把wx代回去,即-π/2w<=x<=π/2w ,[-π/3,π/4]<=[-π/2w,π/2w]的条件下都能满足函数单调递增,所以-π/2w<=-π/3,π/2w>=π/4,连列,解不等式。
那个。。我没具体算。。可能有的地方大于小于号写的不太对。。剩下的一会再写。。
没事,不用急,我学的时候也稀里糊涂,但用着用着就会了,高考就考那几个题型,多问问老师就没问题了
根下 √,你的标准答案有问题啊
道经
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