Question

помогите номер 350.алгебра

Answer 1

$1)sin(alpha+beta)=sin(alpha)cos(beta)+cos(alpha)sin(beta)\0 textless alpha textless 90Rightarrow sin(alpha) textgreater 0Rightarrow sin(alpha)=sqrt{1-cos^2(alpha)}=\=sqrt{1-0.36}=0.8\sin(alpha+30^circ)=0.8*{sqrt3over2}+0.6*{1over2}=0.4sqrt3+0.3\\ 2)cos(alpha+beta)=cos(alpha)cos(beta)-sin(alpha)sin(beta)\0 textless alpha textless 90Rightarrow cos(alpha) textgreater 0Rightarrow cos(alpha)=sqrt{1-sin^2(alpha)}=\=sqrt{1-{1over2}}={sqrt2over2}\cos(alpha+60^circ)={sqrt2over2}*{1over2}-{sqrt2over2}*{sqrt3over2}={sqrt2over4}(1-sqrt3)\\ 3)sin(alpha-beta)=sin(alpha)cos(beta)-cos(alpha)sin(beta)\270 textless alpha textless 360Rightarrow sin(alpha) textless 0Rightarrow sin(alpha)=-sqrt{1-sin^2(alpha)}=\=-sqrt{1-{1over4}}=-{sqrt3over2}\180 textless beta textless 270Rightarrow cos(beta) textless 0Rightarrow cos(beta)=-sqrt{1-sin^2(beta)}=\=-sqrt{1-0.16}=-{0.2sqrt{21}}\sin(alpha-beta)=0.3sqrt7+0.2\cos(alpha+beta)=-0.1sqrt{21}-0.2sqrt3\\ 4)cos(alpha-beta)=cos(alpha)cos(beta)+sin(alpha)sin(beta)\cos(alpha) textless 0Rightarrow cos(alpha)=-sqrt{1-sin^2(alpha)}=-{sqrt5over3}\sin(beta) textless 0Rightarrow sin(beta)=-sqrt{1-cos^2(alpha)}=-{sqrt7over4}\sin(alpha+beta)=-{1over2}+{sqrt{35}over12}\cos(alpha-beta)={sqrt5over4}-{sqrt7over6}$)