(sin1)^2+(sin2)^2+(sin3)^2+...+(sin89)^2=?

来源:学生作业帮助网 编辑:作业帮 时间:2024/05/05 01:16:19
(sin1)^2+(sin2)^2+(sin3)^2+...+(sin89)^2=?

(sin1)^2+(sin2)^2+(sin3)^2+...+(sin89)^2=?
(sin1)^2+(sin2)^2+(sin3)^2+...+(sin89)^2=?

(sin1)^2+(sin2)^2+(sin3)^2+...+(sin89)^2=?
(sin1)^2+(sin2)^2+(sin3)^2+...+(sin89)^2=(sin1)^2+(sin2)^2+(sin3)^2+…+(cos1)^2+(cos2)^2+…(cos44)^2=1+1+…+1+(sin45)^2=44+0.5=44.5
由(sinX)^2+(cosX)^2=1得到的

(sin1)^2+(sin2)^2+(sin3)^2+...+(sin89)^2
=(sin1)^2+(sin2)^2+(sin3)^2+...+(cos1)^2
=1+1+1......+1+(sin45)^2
=44+1/2
=44.5

因为(sinx)^2+sin(90-x)^2=1
所以(sin1°)^2+(sin2°)^2+ (sin3°)^2…… (sin89°)^2
=1*44+(sin45)^2
=44+1/2
=89/2