name: \ndate: \nmc precalculus: section 8.2 & 8.3 practice\n1. give the period and amplitude of each\na. ( y…

name: \ndate: \nmc precalculus: section 8.2 & 8.3 practice\n1. give the period and amplitude of each\na. ( y = 4cos(2x) )\nb. ( y = - 4sinleft(\frac{x}{3}\right) )\nc. ( y = 5sinleft(\frac{2pi}{7}x\right) )\nd. ( y = 1.5cosleft(\frac{pi}{3}x\right) )

Answer

Explanation:

Step1: Recall the formula for amplitude and period

For a function (y = A\sin(Bx)) or (y=A\cos(Bx)), the amplitude is (|A|) and the period is (T=\frac{2\pi}{|B|}).

Step2: Solve for part a

For (y = 4\cos(2x)), (A = 4), (B = 2). Amplitude: (|4|=4). Period: (T=\frac{2\pi}{2}=\pi).

Step3: Solve for part b

For (y=-4\sin(\frac{x}{3})), (A=-4), (B=\frac{1}{3}). Amplitude: (|-4| = 4). Period: (T=\frac{2\pi}{\frac{1}{3}}=6\pi).

Step4: Solve for part c

For (y = 5\sin(\frac{2\pi}{7}x)), (A = 5), (B=\frac{2\pi}{7}). Amplitude: (|5|=5). Period: (T=\frac{2\pi}{\frac{2\pi}{7}}=7).

Step5: Solve for part d

For (y = 1.5\cos(\frac{\pi}{3}x)), (A = 1.5), (B=\frac{\pi}{3}). Amplitude: (|1.5|=1.5). Period: (T=\frac{2\pi}{\frac{\pi}{3}}=6).

Answer:

a. Amplitude: (4), Period: (\pi) b. Amplitude: (4), Period: (6\pi) c. Amplitude: (5), Period: (7) d. Amplitude: (1.5), Period: (6)