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夜雨聆风 > > 办公文件 > @数学教材习题赏析 征解的趣味三角函数题解答

@数学教材习题赏析 征解的趣味三角函数题解答

当前时间： 2026-06-27 22:42:54 分类：办公文件 评论(0)
@数学教材习题赏析 征解的趣味三角函数题解答

宋老师的一个公号 @数学教材习题赏析 刚刚分享了下面这道有趣的三角函数题。

锐角α满足，求α

大眼一瞅，36°属于18°的倍角，还算是个特殊角，但是48°角不太常见，直觉上似乎可以考虑拆成30°+18°，分母里又多出来个系数，并不整齐，和差化积不太有戏，面对这个情况，果断祭出计算器，咔嚓一算，等式右边大约是个0.3249，正是18°角的正切值，于是α = 18°。

答案在手，咱们来个反推，验证一下。

上面最后一个等号是成立的，毕竟、。

上面的验证过程，其实就是化解过程的某种逆过程，受此启发，我们可以装模作样攒个正经步骤

如果没有前面的验证过程，上面步骤里的几处恒等变形不太好想，算是一种投机取巧吧……

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  143. /yingpanguazai/ssd/ssd1/www/wwww.yeyulingfeng.com/vendor/topthink/think-template/src/template/contract/DriverInterface.php ( 0.86 KB )
  144. /yingpanguazai/ssd/ssd1/www/wwww.yeyulingfeng.com/runtime/temp/c935550e3e8a3a4c27dd94e439343fdf.php ( 31.50 KB )
  145. /yingpanguazai/ssd/ssd1/www/wwww.yeyulingfeng.com/vendor/topthink/think-trace/src/Html.php ( 4.42 KB )
  1. CONNECT:[ UseTime:0.000654s ] mysql:host=127.0.0.1;port=3306;dbname=wenku;charset=utf8mb4
  2. SHOW FULL COLUMNS FROM `fenlei` [ RunTime:0.001019s ]
  3. SELECT * FROM `fenlei` WHERE `fid` = 0 [ RunTime:0.000414s ]
  4. SELECT * FROM `fenlei` WHERE `fid` = 63 [ RunTime:0.000298s ]
  5. SHOW FULL COLUMNS FROM `set` [ RunTime:0.000667s ]
  6. SELECT * FROM `set` [ RunTime:0.000255s ]
  7. SHOW FULL COLUMNS FROM `article` [ RunTime:0.000728s ]
  8. SELECT * FROM `article` WHERE `id` = 807085 LIMIT 1 [ RunTime:0.000548s ]
  9. UPDATE `article` SET `lasttime` = 1782635225 WHERE `id` = 807085 [ RunTime:0.008239s ]
  10. SELECT * FROM `fenlei` WHERE `id` = 64 LIMIT 1 [ RunTime:0.000387s ]
  11. SELECT * FROM `article` WHERE `id` < 807085 ORDER BY `id` DESC LIMIT 1 [ RunTime:0.000678s ]
  12. SELECT * FROM `article` WHERE `id` > 807085 ORDER BY `id` ASC LIMIT 1 [ RunTime:0.000523s ]
  13. SELECT * FROM `article` WHERE `id` < 807085 ORDER BY `id` DESC LIMIT 10 [ RunTime:0.000978s ]
  14. SELECT * FROM `article` WHERE `id` < 807085 ORDER BY `id` DESC LIMIT 10,10 [ RunTime:0.002493s ]
  15. SELECT * FROM `article` WHERE `id` < 807085 ORDER BY `id` DESC LIMIT 20,10 [ RunTime:0.006169s ]
0.111224s