3/5=sin(x+π/4) 求sinx

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3/5=sin(x+π/4) 求sinx

3/5=sin(x+π/4) 求sinx
3/5=sin(x+π/4) 求sinx

3/5=sin(x+π/4) 求sinx
sin(x+π/4)
=sinx*cosπ/4+cosx*sinπ/4
=根号2/2[sinx+cosx]
=3/5
所以sinx+cosx=(3根号2)/5
又因为sinx^2+cosx^2=1
sinx=(7根号2)/10或-(根号2)/10

sin(x+π/4)=64°

因为 sin(x+π/4)=3/5
所以 cos(x+π/4)=±4/5
sinx=sin(x+π/4-π/4)
=sin(x+π/4)cosπ/4-cos(x+π/4)sinπ/4
=√2/2(sin(x+π/4)-cos(x+π/4))
=√2/2(3/5±4/5)
所以 sinx=-√2/10 或 sinx=7√2/10