Question

g(x)=sin 1,5x +5 cos(3/4)x . Найти g(7pi)

Answer 1

$g(7 pi )=sin(1.5*7 pi )+5cos( frac{3}{4}*7 pi )=sin10.5 pi +5cos frac{21 pi }{4}= \ \ =sin frac{21}{2} pi +5cos( frac{20 pi }{4}+ frac{ pi }{4} )=sin( frac{20 pi }{2}+ frac{ pi }{2} )+5cos(5 pi + frac{ pi }{4} )= \ \ =sin(10 pi + frac{ pi }{2} )+5*(-cos frac{ pi }{4} )=sin frac{ pi }{2}-5* frac{ sqrt{2} }{2} =1- frac{5 sqrt{2} }{2}= frac{2-5 sqrt{2} }{2}$