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

Решите задачу:

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