Find the amplitude and period of the function. $y = 4 \sin(−6x)$

Question

Do I factor the $-6$ out then divide $2π/-6$ to get the period?

Answer 1

I find helpful to think about physics here. If you have a periodic function like $\sin$ or $\cos$, a wave is given by $$y(x,t) = A\cos(kx - \omega t + \phi)$$ and the period is given by $T = 2\pi /\omega$. Also the wave length is given by $\lambda = 2 \pi/ k$.

Now, to your specific problem, $y = 4 \sin (-6x)$ would wield an amplitude equal to $4$, and period $2 \pi /6 = \pi/3$, since periods are always positive. Ok?

Answer 2

Note that $f(x) = 4\sin(-6x) = -4\sin(6x)$. Thus, $T = \dfrac{2\pi}{6} = \dfrac{\pi}{3}$. The amplitude is $A = 4$.