Question

найдите значения выражений

Answer 1

$2)frac{2Cos(-2pi-beta)+Sin(-frac{pi }{2}+beta)}{2Cos(beta+pi)}=frac{2Cos(2pi+beta)-Sin(frac{pi}{2}-beta)}{2Cos(pi+beta)}=frac{2Cosbeta-Cosbeta}{-2Cosbeta}=-frac{Cosbeta}{2Cosbeta}=-frac{1}{2}=-0,5$

$3)-15Cos(frac{7pi }{2}-alpha)=-15Cos[4pi-(frac{pi }{2}+alpha)]=-15Cos(frac{pi }{2}+alpha )=-15*(-Sinalpha)=15Sinalpha\\1,5pi<alpha<2pi Rightarrow Sinalpha<0\\Sinalpha=-sqrt{1-Cos^{2}alpha}=-sqrt{1-(frac{7}{25})^{2}}=-sqrt{1-frac{49}{625} }=-sqrt{frac{576}{625}}=-frac{24}{25}\\15Sinalpha=15*(-frac{24}{25} )=- 14,4$

$4)tg(alpha-frac{pi }{2})=-tg(frac{pi }{2}-alpha)=-Ctgalpha\\-Ctgalpha=-frac{1}{tgalpha}=-frac{1}{0,04}=-25$