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已知F(X)=Asinx+Btanx+3满足F(五分之派)=5,则F(五分之九十九派)=多少

题目详情
已知F(X)=Asinx+Btanx+3满足F(五分之派)=5,则F(五分之九十九派)=多少
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答案和解析
∵f(π/5)=Asinπ/5+Btanπ/5+3=5,∴Asinπ/5+Btanπ/5=2,∴f(99π/5)=Asin99π/5+Btan99π/5+3=Asin(20π-π/5)+Btan(20π/5)+3=-Asinπ/5-Btanπ/5+3=-(Asinπ/5+Btanπ/5)+3=-2+3=1
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