计算:Sin30°-(根号2)sin45°+4/3sin²60°+sin²30°+sin270°急用

问题描述:

计算:
Sin30°-(根号2)sin45°+4/3sin²60°+sin²30°+sin270°
急用

Sin30°-(根号2)sin45°+4/3sin²60°+sin²30°+sin270°
=1/2-(根号2)*(根号2)/2 +4/3*[(根号3)/2]^2+(1/2)^2+(-1)
=1/2 -1+4/3(3/4)+1/4 -1
=-1/4
()^2 是()内的平方的意思 (1/2)^2=1/4 [(根号3)/2]^2=3/4

因为sin(30度45度60度270度)的值分别是1/2;二分之根号二;二分之根号三;-1所以代入得:三分之二乘跟号三减1

Sin30°-√2sin45°+4/3sin²60°+sin²30°+sin270°
=1/2-√2*(√2)/2+4/3*[(√3)/2]^2+(1/2)^2+(-1)
=1/2-1+1+(1/4)-1
=-(1/4)