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f(x)=sin(x+四分之七乘以派)+cos(x-四分之三乘以派),求f(x)最小正周期及最小值?,
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f(x)=sin(x+四分之七乘以派)+cos(x-四分之三乘以派),求f(x)最小正周期及最小值?,
▼优质解答
答案和解析
f(x)=sin(x+7π/4)+cos(x-3π/4)
=sinxcos7π/4+cosxsin7π/4+cosxcos3π/4+sinxsin3π/4
=sinx√2/2-cosx√2/2-cosx√2/2+sinx√2/2
=√2(sinx-cosx)
=2sin(x-π/4)
T=2π/1=2π,
fmin(x)=-2
=sinxcos7π/4+cosxsin7π/4+cosxcos3π/4+sinxsin3π/4
=sinx√2/2-cosx√2/2-cosx√2/2+sinx√2/2
=√2(sinx-cosx)
=2sin(x-π/4)
T=2π/1=2π,
fmin(x)=-2
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