Question

求一道函数题？

sin^2(1°)+sin^2(2°)+sin^2(3°)+sin^2(4°)+……sin^2(46°)+……sin^2(89°)
详细解答。并能让我明白。写得好可以加分

Answer 1

sin(89°)=cos(1°)
sin(88°)=cos(2°)
以此类推，则原式变为
sin^2(1°)+sin^2(2°)+sin^2(3°)+sin^2(4°)+……sin^2(45°)+……+cos^2(88°)+cos^2(89°)
因为sin^2(X）+cos^2(X)=1
所以原式等于1+1+……+sin^2(45°)=44+1/2=44.5
我的想法是这样，能不能理解就看你了

Answer 2

sin x = cos (90° - x)

sin^2(1°)+sin^2(2°)+sin^2(3°)+sin^2(4°)+……sin^2(46°)+……sin^2(89°)

= sin^2(1°)+sin^2(2°)+sin^2(3°)+sin^2(4°)+……+sin^2(44°)
+ sin^2(45°)
+ sin^2(46°)+……+sin^2(89°)

= sin^2(1°)+sin^2(2°)+sin^2(3°)+sin^2(4°)+……+sin^2(44°)
+ sin^2(45°)
+ cos^2(44°)+cos^2(43°)+……+cos^2(1°)

= 1+1+1+1+……+1 + sin^2(45°)

= 44+1/2

= 89/2.