3 True or False 1 point Verify thatsin \( 2 A-\tan A=\tan A \cos 2 A \) is an identity. (1) True (D) False

What is the period of \( y=\sin (3 x) \) ? \( \begin{array}{l}\frac{\pi}{3} \\ \frac{2 \pi}{3} \\ 3 \pi \\ 6 \pi\end{array} \)

What is the general equation of a cosine function with an amplitude of 3 , a period of \( 4 \pi \), and a horizontal shift of \( -\pi \) ? \( \begin{array}{l}y=4 \pi \cos (3(x-\pi)) \\ y=3 \cos (4 \pi(x+\pi)) \\ y=3 \cos (0.5(x+\pi)) \\ y=4 \pi \cos (0.2(x+\pi))\end{array} \)

The equation \( h=7 \sin \left(\frac{\pi}{21} t\right)+28 \) can be used to model the height, \( h \), in feet of the end of one blade of a windmill turning on an axis above the ground as a function of time, \( t \), in seconds. How long is the blade? Assume that the blade is pointing to the right, parallel to the ground, at \( t=0 \), and that the windmill turns counterclockwise at a constant rate. 7 feet 14 feet 21 feet 28 feet

The displacement, \( d \), in millimeters of a tuning fork as a function of time, \( t \), in seconds can be modeled with the equation \( d=0.4 \sin (1760 \pi f) \). What is the maximum displacement of the tuning fork? 0.2 mm 0.4 mm 0.8 mm 2.5 mm

Prove the following trigonometric identity: \( \frac{\sin A\left[1-\sin \left(360^{\circ}-A\right)\right]}{1-\cos ^{2}\left(180^{\circ}+A\right)}-1=\operatorname{cosec} A \)