asin(θ+α)+bsin(θ+β)=?化简f(x)=asin(πx+α)+bcos(πx+β)且f(2009)=3,则f(2010)=?

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asin(θ+α)+bsin(θ+β)=?化简f(x)=asin(πx+α)+bcos(πx+β)且f(2009)=3,则f(2010)=?

asin(θ+α)+bsin(θ+β)=?化简f(x)=asin(πx+α)+bcos(πx+β)且f(2009)=3,则f(2010)=?
asin(θ+α)+bsin(θ+β)=?
化简
f(x)=asin(πx+α)+bcos(πx+β)
且f(2009)=3,则f(2010)=?

asin(θ+α)+bsin(θ+β)=?化简f(x)=asin(πx+α)+bcos(πx+β)且f(2009)=3,则f(2010)=?
答案为-3
因为asin(θ+α)和bsin(θ+β)的周期都为2π,所以f(2009)=asin(2009π+α)+bcos(2009π+β)=
asin(π+α)+bcos(π+β)=3,再利用诱导公式
f(2010)=asin(2010π+α)+bcos(2010π+β)=asinα+bcosβ=-asin(π+α)-bcos(π+β)=-3