Question

8. Решить уравнение:cos (3x+π/4)=√3/2

9.Решить уравнение:2 〖sin〗^2 x-sin x=0

10.Решить уравнение:6-6 〖sin〗^2 x+5 sin⁡x=7

11.Решить уравнение: 3 〖sin〗^2 2x-0,5 sin 4x=4

Answer 1

8)

$cos(3x frac{pi}{4})=frac{sqrt{3}}{2}\ 3x frac{pi}{4}=frac{pi}{3} 2pi k kin Z\ 3x=frac{pi}{12} 2pi k kin Z\ x=</var>frac{pi}{36} frac{2pi k}{3} kin Z$</p> <p>или </p> <p><img src=[/tex]3x+frac{pi}{4}=frac{5pi}{6}+2pi k kin Z\ 3x=frac{7pi}{12}+2pi k kin Z\ x=frac{7pi}{36}+frac{2pi k}{3} kin Z" title="cos(3x+frac{pi}{4})=frac{sqrt{3}}{2}\ 3x+frac{pi}{4}=frac{pi}{3}+2pi k kin Z\ 3x=frac{pi}{12}+2pi k kin Z\ x=frac{pi}{36}+frac{2pi k}{3} kin Z" title="3x+frac{pi}{4}=frac{5pi}{6}+2pi k kin Z\ 3x=frac{7pi}{12}+2pi k kin Z\ x=frac{7pi}{36}+frac{2pi k}{3} kin Z" title="cos(3x+frac{pi}{4})=frac{sqrt{3}}{2}\ 3x+frac{pi}{4}=frac{pi}{3}+2pi k kin Z\ 3x=frac{pi}{12}+2pi k kin Z\ x=frac{pi}{36}+frac{2pi k}{3} kin Z" alt="3x+frac{pi}{4}=frac{5pi}{6}+2pi k kin Z\ 3x=frac{7pi}{12}+2pi k kin Z\ x=frac{7pi}{36}+frac{2pi k}{3} kin Z" title="cos(3x+frac{pi}{4})=frac{sqrt{3}}{2}\ 3x+frac{pi}{4}=frac{pi}{3}+2pi k kin Z\ 3x=frac{pi}{12}+2pi k kin Z\ x=frac{pi}{36}+frac{2pi k}{3} kin Z" />

или 

$cos(3x+frac{pi}{4})=frac{sqrt{3}}{2}\ 3x+frac{pi}{4}=frac{pi}{3}+2pi k kin Z\ 3x=frac{pi}{12}+2pi k kin Z\ x=</var>frac{pi}{36}+frac{2pi k}{3} kin Z$

или 

$<var>3x frac{pi}{4}=frac{5pi}{6} 2pi k kin Z\ 3x=frac{7pi}{12} 2pi k kin Z\ x=frac{7pi}{36} frac{2pi k}{3} kin Z$

 

Ответ:{ $frac{pi}{36}+frac{2pi k}{3} kin Z" title="<var>3x+frac{pi}{4}=frac{5pi}{6}+2pi k kin Z\ 3x=frac{7pi}{12}+2pi k kin Z\ x=frac{7pi}{36}+frac{2pi k}{3} kin Z" /></var></p> <p> </p> <p>Ответ:{ [tex]frac{pi}{36}+frac{2pi k}{3} kin Z" alt="<var>3x+frac{pi}{4}=frac{5pi}{6}+2pi k kin Z\ 3x=frac{7pi}{12}+2pi k kin Z\ x=frac{7pi}{36}+frac{2pi k}{3} kin Z" /></var></p> <p> </p> <p>Ответ:{ [tex]frac{pi}{36}+frac{2pi k}{3} kin Z" /> ; [tex]frac{7pi}{36}+frac{2pi k}{3} kin Z$}

 

9)

$2sin^{2}x-sinx=0\ sinx(2sinx-1)=0\ \sinx=0\ x=pi k k in Z$

или 

$\sinx=0,5\ x=frac{pi}{4}+2pi k k in Z\ \ x=frac{3pi}{4}+2pi k k in Z$

 

Ответ:{$pi k k in Z$  ; $frac{pi}{4}+2pi k k in Z$  ; $frac{3pi}{4}+2pi k k in Z$ }