shijuedengludizhi6:河南省长垣县第十中学高中数学必修4课件:1.4.3正切函数(第二课时)_图文

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学.科.网 第二课时 ? ? ? 定义域: ? x x ? ? k? , k ? Z ? 2 ? ? 正切函数的性质 : 值域: R 周期性:T ? ? 奇偶性:奇函数 ? ? ? ? 单调性: 在开区间 ? ? ? k? , ? k? ? k ? Z内递增 2 ? 2 ? 在每一个开区间内都是单调增函数.能不能说 正切函数在整个定义域上单调递增? ?? ? 例1、已知函数y ? t an? ? 2 x ? ?,求: 3? ? ( 1 )函数的定义域、值域 、周期; ( 2 )求函数的对称中心; ( 3 )求函数的单调区间 . ?? ? 变式:已知函数 y ? sin ? ? 2 x ? ?,求: 3? ? ( 1 )函数的定义域、值域 、周期; ( 2 )求函数的对称轴; ( 3 )求函数的单调增区间 . 13 17 例2、比较 tan ?与 tan ?的大小 . 4 5 π π 析 : 利用y ? tan x在( ? , )上是增函数。 2 2 例3 若 ?1 ? tan x ? 3,求x 的取值范 围. 变式:求函数 y ? tan x ? log2 x(2 ? x)的定义域。 变式:已知函数 f ( x) ? x 2 ? 2 x ? tan? ? 1在区间 [?1, 3 ] 上是单调函数,求 ?的取值范围。 变式:试讨论函数 y ? loga tan x的单调性 zxxkw

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