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2019高中数学人教A版必修4习题:第一章三角函数 1.3.1

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∴f(α)=cosα= - = -

(3) - - =co - ★

8设f(x)=asin(πx+α)+bcos(πx+β)+7,α,β均为实数,若f(2 017)=6,求f(2 018)的值.

解∵f(2017)=asin(2017π+α)+bcos(2017π+β)+7

=-asinα-bcosβ+7,

∴-asinα-bcosβ+7=6,∴asinα+bcosβ=1. 又f(2018)

=asin(2018π+α)+bcos(2018π+β)+7 =asinα+bcosβ+7, ∴f(2018)=1+7=8.

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