Sketch a graph of the function \( f(x)=2 \sin (2 x) \).

If \( \tan \left(3 \theta-70^{\circ}\right) \times \tan \theta=1 \) where \( \left.\theta \in\right] 0, \frac{\pi}{3}[ \), then \( \sin (2 \theta+10)= \)

Identify the transformations for the function \( f(x)=3 \cos \left(-x+\frac{\pi}{3}\right)-2 \). ( 1 point) vertical stretch by a factor of 3 , reflection over the \( y \)-axis, horizontal shift right by \( \frac{\pi}{3} \), and vertical shift down 2 vertical stretch by a factor of 3 , reflection over the \( y \)-axis, horizontal shift right by \( \frac{\pi}{3} \), and vertical shift up 2 vertical stretch by a factor of 3 , horizontal compression by -1 , horizontal shift night by \( \frac{\pi}{3} \), and . vertical shift down 2 vertical stretch by a factor of 3 , reflection over the \( y \)-axis, horizontal shift left by \( \frac{\pi}{3} \), and vertical shift down 2

9.1 Determine the general solutions of: \( 2 \cos ^{2} \alpha+5 \sin \alpha=4 \) \( \sin \alpha=2 \)

Which of the following correctly describes the phase shift of the function \( f(x)=2 \sin \left(x+\frac{\pi}{6}\right) \) ? (1 point) \( 0 . \frac{\pi}{6} \) \( \frac{\pi}{2} \)

Find the amplitude, period, and phase shift of the function. Graph the function. Be sure to label key points. Show at least two periods. \( y=6 \) cos \( \left(2 x-\frac{\pi}{2}\right) \) What is the amplitude? (Simplify your answer. Type an exact answer, using \( \pi \) as needed. Use integers or fractions for any numbers in the expression.) What is the period? \( \square \) (Simplify your answer. Type an exact answer, using \( \pi \) as needed. Use integers or fractions for any numbers in the expression.) What is the phase shift? \( \square \)