上海高中數(shù)學(xué)三角函數(shù)大題壓軸題練習(xí)

1、三角函數(shù)大題壓軸題練習(xí)1已知函數(shù)()cos(2)2sin()sin()344fxxxx????????（Ⅰ）求函數(shù)的最小正周期和圖象的對(duì)稱軸方程()fx（Ⅱ）求函數(shù)在區(qū)間上的值域()fx[]122???解：（解：（1）()cos(2)2sin()sin()344fxxxx?????????13cos2sin2(sincos)(sincos)22xxxxxx?????2213cos2sin2sincos22xxxx????13cos2si

2、n2cos222xxx???sin(2)6x???2T2????周周∴由2()()6223kxkkZxkZ????????????周函數(shù)圖象的對(duì)稱軸方程為∴()3xkkZ?????（2）5[]2[]122636xx????????????因?yàn)樵趨^(qū)間上單調(diào)遞增，在區(qū)間上單調(diào)()sin(2)6fxx???[]123???[]32??遞減，所以當(dāng)時(shí)，取最大值13x??()fx又，當(dāng)時(shí)，取最小值31()()12222ff????????12x?

3、??()fx32?所以函數(shù)在區(qū)間上的值域?yàn)?)fx[]122???3[1]2?2已知函數(shù)（）的最小正周期為2π()sin3sinsin2fxxxx????????????0??π（Ⅰ）求的值；?4.已知函數(shù)，的最大值是1，其圖像經(jīng)過點(diǎn)()sin()(00π)fxAxA???????，x?R（1）求的解析式；（2）已知，且，π132M??????，()fxπ02?????????，，3()5f??，求的值12()13f??()f???【解

4、析】（1）依題意有，則，將點(diǎn)代入得1A?()sin()fxx???1()32M?，而，，，故1sin()32????0????536??????2????；()sin()cos2fxxx????（2）依題意有，而，312coscos513????(0)2????，2234125sin1()sin1()551313?????????。3124556()cos()coscossinsin51351365f??????????????????

5、5.已知函數(shù)117()()cos(sin)sin(cos)().112tftgxxfxxfxxt??????????（Ⅰ）將函數(shù)化簡(jiǎn)成（，，）的形式；()gxsin()AxB????0A?0??[02)???（Ⅱ）求函數(shù)的值域.()gx解.本小題主要考查函數(shù)的定義域、值域和三角函數(shù)的性質(zhì)等基本知識(shí)，考查三角恒等變換、代數(shù)式的化簡(jiǎn)變形和運(yùn)算能力.（滿分12分）解：（Ⅰ）1sin1cos()cossin1sin1cosxxgxxxxx???