問：不用計算機，求 cos
π/11 + cos
3π/11 +
cos 5π/11 +
cos 7π/11 +
cos 9π/11 的值。
解：
(sin π/11)(cos π/11 + cos 3π/11 + cos 5π/11 + cos 7π/11
+ cos 9π/11) ÷
(sin π/11)
= [(0.5)(sin 2π/11 + sin 0 + sin 4π/11 - sin 2π/11
+ sin 6π/11 - sin 4π/11 +
sin 8π/11 - sin 6π/11 + sin 10π/11 - sin 8π/11)] ÷ (sin π/11)
= (0.5)(sin 10π/11) ÷ (sin π/11)
= (0.5)(sin π/11) ÷ (sinπ/11) [Note: sin 10π/11 = sin (π - 10π/11) = sin π/11]
= 0.5
(這條想了近三個小時才想到~~~
)
全站熱搜
留言列表
