(1/2)已知向量m=(sinA,cosA)n=(1,-2)且m.n=0 (1)求tanA的值 (2)求函数f(x)=cos2x+tanAs
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(1/2)已知向量m=(sinA,cosA)n=(1,-2)且m.n=0 (1)求tanA的值 (2)求函数f(x)=cos2x+tanAs
(1/2)已知向量m=(sinA,cosA)n=(1,-2)且m.n=0 (1)求tanA的值 (2)求函数f(x)=cos2x+tanAs
(1/2)已知向量m=(sinA,cosA)n=(1,-2)且m.n=0 (1)求tanA的值 (2)求函数f(x)=cos2x+tanAs
(1)sinA-2cosA=0.∴tanA=2
(2)cos2x+tanAsinx=(1-2sin²x)+2sinx=-2(sinx-1/2)²+(3/2)
∴当sinx=1/2,即x=π/6+2kπ或x=5π/6 +2kπ,k∈Z,有最大值3/2
当sinx=-1,即x=3π/2 +2kπ有最小值y=-3
∴[-3,3/2]
(1)你懂
(2)f(x)=cos2x+tanAsinx=1-2sin²x+2sinx,令sinx=t,-1<=t<=1,则f(x)=-2t²+2t+1,下面提供两种思路:1.配方法:f(x)=-2(t-1/2)²+3/2,所以t=1/2时取最大值3/2,t=-1时取最小值-3
2.求导法。字数限制啊。
m.n=0=>sinA-2 cosA=0=>sinA/cosA=2=>tanA=2
f(x)=cos2x+tanA=>f(x)=cos2x+2