Question

（本小题满分12分）

如图，在平面直角坐标系中，锐角的终边分别与单位圆交于两点．

         （Ⅰ）如果，点的横坐标为，求的值；

         （Ⅱ）已知点，求函数的值域．

Answer

（Ⅰ）．

（Ⅱ）函数的值域为．

【解析】(I)根据三角函数的定义及同角的三角函数关系式可求出和, 因是锐角,可求出

然后根据两角和的余弦公式求解即可.

(2)解本小题的关系是先求出

然后根据, 确定出, 进而求出的值域.

（Ⅰ）∵ 是锐角，，

∴ ．·············································································· 2分

根据三角函数的定义，得，

又∵ 是锐角，

∴ ．············································································· 4分

∴ ．························ 6分

（Ⅱ）由题意可知，，．

∴ ，····································· 8分

∵ ，

∴ ，························································································ 9分

∴ ，从而，······································ 11分

∴ 函数的值域为． 12分