已知sin(a+π/4)=4/5,且π/4

来源:学生作业帮助网 编辑:作业帮 时间:2024/07/29 10:25:05
已知sin(a+π/4)=4/5,且π/4
xQKN0N|N8A Vݔ@UVn` Q:Fgl\Tl/U{$PPeJ3ڤ(#knw_}sdQOrm4@c=_4 QA:T,Dy6F@.5+H: .K3@YzP st '7HhKedyklV EO oq'K/iՅ

已知sin(a+π/4)=4/5,且π/4
已知sin(a+π/4)=4/5,且π/4

已知sin(a+π/4)=4/5,且π/4
π/4其实
π/4因为如果
a>π/2,sin(a+π/4)<根号2
π/2cos(a+π/4)=-3/5
cos(2*a)=sin(2*a+π/2)=sin2*(a+π/4)=2*sin(a+π/4)*cos(a+π/4)=-24/25
cos(2*a)=2*(cosa)^2-1
cosa=根号0.02

π/4π/2cos(a+π/4)=-3/5.
cosa=cos[(a+π/4)-π/4]=cos(a+π/4)cosπ/4+sin(a+π/4)sinπ/4
=(-3/5)*(√2/2)+4/5*√2/2
=√2/10.