Question

$-\frac{15sin(x)}{2} -\frac{15}{4} =0$
помогите решить

Answer 1

$-\dfrac{15\sin x}{2} -\dfrac{15}{4}=0$

$-\dfrac{15\sin x}{2} =\dfrac{15}{4}$

$-\sin x =\dfrac{1}{2}$

$\sin x =-\dfrac{1}{2}$

$x = (-1)^{n}\arcsin\bigg(-\dfrac{1}{2} \bigg) + \pi n, \ n \in Z\\\\x = (-1)^{n} \cdot \bigg(-\dfrac{\pi}{6} \bigg)+ \pi n, \ n \in Z\\\\x = (-1)^{n} \cdot (-1) \cdot \dfrac{\pi}{6}+ \pi n, \ n \in Z\\\\x = (-1)^{n+1}\cdot \dfrac{\pi}{6}+ \pi n, \ n \in Z$

Ответ: $x = (-1)^{n+1}\cdot \dfrac{\pi}{6}+ \pi n, \ n \in Z$