①求y=cos(1/2x-π/6)的对称轴和对称中心 ②求y=sin(-1/2x+π/3)在区间[-π,π]的最值
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①求y=cos(1/2x-π/6)的对称轴和对称中心 ②求y=sin(-1/2x+π/3)在区间[-π,π]的最值
①求y=cos(1/2x-π/6)的对称轴和对称中心 ②求y=sin(-1/2x+π/3)在区间[-π,π]的最值
①求y=cos(1/2x-π/6)的对称轴和对称中心 ②求y=sin(-1/2x+π/3)在区间[-π,π]的最值
①对称轴过最高/低点
∴cos(1/2x-π/6)=±1
∴x/2-π/6=kπ
∴x=2kπ+π/3 (k∈z)
∴对称轴x=2kπ+π/3 (k∈z)
对称中心在x轴上
∴cos(1/2x-π/6)=0
∴x/2-π/6=kπ+π/2
∴x=2kπ+4π/3(k∈z)
∴对称中心坐标(2kπ+4π/3,0)(k∈z)
②当-1/2x+π/3=-π/6时,y为最小值
即x=π时,y=-1/2
当-1/2x+π/3=π/2时,y为最大值
即x=-π/3时,y=1
①
y=cos(1/2x-π/6)
由1/2x-π/6=kπ,k∈Z得
对称轴方程 x=2kπ+π/3,k∈Z
由1/2x-π/6=kπ+π/2,k∈Z得
x=2kπ+4π/3,k∈Z
∴对称中心为(2kπ+4π/3,0) k∈Z
②
y=sin(-1/2x+π/3)
∵[-π,π]
∴-π/2≤-1/2x≤π/2...
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①
y=cos(1/2x-π/6)
由1/2x-π/6=kπ,k∈Z得
对称轴方程 x=2kπ+π/3,k∈Z
由1/2x-π/6=kπ+π/2,k∈Z得
x=2kπ+4π/3,k∈Z
∴对称中心为(2kπ+4π/3,0) k∈Z
②
y=sin(-1/2x+π/3)
∵[-π,π]
∴-π/2≤-1/2x≤π/2
∴ -π/6≤-1/2x +π/3≤5π/6
∴当-1/2x +π/3=-π/6,即x=π时,y取得最小值-1/2
当-1/2x +π/3=π/2,即x=-π/3时,y取得最小值1
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