题目

The question this week comes from our listener Herve Acard, who asks about the American word “OK”, which means “all right” or “acceptable”. It expresses agreement or approval. The word is used more often than any other word in the world. Language expert Allen Walker Read said the word began as a short way of writing a different spelling of the words “all correct”. Old stories say some foreign-born people would write “all correct” as o-l-l k-o-r-r-e-c-t and spoke it as “OK”. Some people say it came from the Native American Indian tribe known as the Choctaws. The设A是单位圆和x轴正半轴的交点，P，Q是单位圆上两点，O是坐标原点，且∠AOP=β，β∈（0，π2），∠AOQ=α，α∈[0，π）．（1）若点Q的坐标是 （m，45），其中m＜0，求cos（π-α）+sin（-α）的值．（2）设P（32，12），函数f（α）=sin（α+β），求f（α）的值域．