函数对称轴函数y=sin2x+acos2x图像关于直线x=-π/8对称,求a!
A.根号2 B.-根号2 C.1 D.-1
解:y=sin2x+acos2x
=[√(1+a^)][(sin2x)×(1/√(1+a^)+(cos2x)×a/√(1+a^)]
sinβ=1/√(1+a^) cosβ=a/√(1+a^)
y=[√(1+a^)]sin(2x+β)
2x+β=π/2 -π2/8+β=π/2
β=3π/4
sinβ=1/√(1+a^)=sin(3π/4)=√2/2
a^=1
∵β=3π/4 ∴ cosβ=a/√(1+a^)<0
∴a=-1
。
解:y=sin2x+acos2x
=[√(1+a^)][(sin2x)×(1/√(1+a^)+(cos2x)×a/√(1+a^)]
sinβ=1/√(1+a^) cosβ=a/√(1+a^)
y=[√(1+a^)]sin(2x+β)
2x+β=π/2 -π2/8+β=π/2
β=3π/4
sinβ=1/√(1+a^)=sin(3π/4)=√2/2
a^=1
∵β=3π/4 ∴ cosβ=a/√(1+a^)<0
∴a=-1
。
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