Use the sum-to-product identities to rewrite the expression as a product. Simplify if possible. \[ \sin 9 x+\sin (-5 x) \]

o 2. Даны комплексные числа \( z_{1}=1-i \sqrt{3} \) и \( z_{2}=-2 \mathrm{i} \). Найти: а) \( z_{1}^{5}, \sqrt[3]{z_{2}} ; \) выполнить действия в тригонометрической форме; результат заппсать в алгебраической форме, в показательной форме; б) изобразить на комплексной плоскости числа \( z_{2} \overline{z_{2}} \); указать на чертеже их модули и аргументы.

Which of the following correctly describes the phase shift of the function \( f(x)=\cos \left(3 x-\frac{\pi}{2}\right) ?(1 \) point) \( -\frac{\pi}{6} \) \( \frac{\pi}{6} \) \( \frac{\pi}{2} \) \( \frac{3 \pi}{2} \)

f) \( 3 \tan ^{3} x-\tan x=0 \)

A periodic function passes through the origin and then descends to a minimum of \( -\frac{2}{3} \) when \( x=\frac{\pi}{2} \). It passes through the x-axis again when \( x=\pi \) and rises to a maximum of \( \frac{2}{3} \) when periodic function? (1 point) \( y=-\frac{2}{3} \cos x \) \( y=\frac{2}{3} \sin x \) \( y=\frac{4}{3} \sin x \) \( y=-\frac{2}{3} \sin x \)

Rewrite the cosine function \( f(x)=-3 \cos \left(x-\frac{\pi}{8}\right)+2 \) as a translated sine function. \( \begin{array}{l}\text { (1 point) } \\ f(x)=-3 \sin \left(x+\frac{\pi}{4}\right)+2 \\ f(x)=-3 \sin \left(x+\frac{\pi}{24}\right)+2 \\ f(x)=-3 \sin \left(x+\frac{3 \pi}{8}\right)+2 \\ f(x)=-3 \sin \left(x-\frac{5 \pi}{8}\right)+2\end{array} \)