高中三角函数
\u9ad8\u4e2d\u4e09\u89d2\u51fd\u6570(1)
\u8bbea/sinA=b/sinB=c/sinC=k
(2c-b)/a=(2ksinC - ksinB)/(ksinA)=(2sinC-sinB)/sinA
\u2234(2sinC-sinB)/sinA=cosB/cosA
\u5373sinAcosB=(2sinC-sinB)cosA=2sinCcosA-sinBcosA
\u5373sinAcosB+sinBcosA=2sinCcosA
\u5373sin(A+B)=2sinCcosA
\u5373sinC=2sinCcosA
\u2234cosA=1/2
A=60\u00b0
(2)
\u2235a/sinA=b/sinB=C/sinC=2\u221a5/(\u221a3/2)=4\u221a5/\u221a3
\u2234(bc)/(sinBsinC)=(4\u221a5/\u221a3)²=80/3
bc=(80/3)sinBsinC
S\u25b3ABC
=(1/2)bcsinA
=(1/2)\u00d7(80/3)sinBsinC\u00d7(\u221a3/2)
=(10/\u221a3)\u00d7(2sinBsinC)
=(10/\u221a3)\u00d7[cos(B-C)-cos(B+C)]
=(10/\u221a3)\u00d7[cos(B-C)+(1/2)]
\u2264(10/\u221a3)\u00d7[1+(1/2)]=5\u221a3
\u5f53\u4e14\u4ec5\u5f53B=C=60\u00b0\u65f6\u7b49\u53f7\u6210\u7acb
\u2234\u5f53B=C=60\u00b0\u65f6\uff0cSmax=5\u221a3
1.f(x)=2cos2x+sin^2x
=2cos2x+(1-cos2x)/2
=3/2(cos2x)+1/2
=3/2(2cos^2x-1)+1/2
=3cos^2x-1
f(\u03c0/3)=-1/4
2.\u5f53cosx=\u00b11\u65f6 f(x)\u6700\u5927\u4e3a2
\u5f53cosx=0\u65f6\uff0cf(x)\u6700\u5c0f\u4e3a-1
cos100=-k
sin100=根号（1-k^2)
tan100=sin100/cos100=-根号（1-k^2)/k
cos80°=cos(-80°)=K,
sin80°=(1-K*K)^(1/2)
tan100°=-tan80°=-(1-K*K)^(1/2) /K
cos(-80)=k 所以cos（100）= -k 所以设斜边为1，邻边为k，对边为根号下1-k方，所以tan100=对边比邻边，记得结果加负号
cos(-80)=cos(80)=k,tan100=-tan(80)=-k/(1-k*k)^(1/2)
cos(100)=-cos80= - cos(-80)=-k
sin100=根号（1-cos100*cos100）=根号（1-k^2）
tan100=sin100/cos100=根号（1-k^2）/-k
cos(-80)=cos80=sin100=k
sin80=-cos100=-根号下1-k的平方
tan100=sin100除以cos100=-(k除以根号下1-k的平方)
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