How do you find the amplitude and period of a function #y = sin (pix - 1/2)#?

Question

Carter Anderson · Accepted Answer

Amplitude: 1
Period: 2

Sin functions are written on a common form: #A sin(bx + c) + d# Where A signifies the amplitude (#"top value - bottom value"/2#) b affects the frequency c signifies the horisontal shift d signifies the vertical shift You can find the amplitude by looking at the coifficient before #"sin"#. In this case, the amplitude is 1. The period is defined by #(2pi)/b# In this case: #(2pi) / pi = (2cancel(pi))/(cancel(pi)) = 2#

Abigail Armstrong · Answer

undefined To find the amplitude and period of the function $y = \sin(\pi x - \frac{1}{2})$:

1. **Amplitude**: The amplitude of a sine function is the absolute value of the coefficient of the sine term, which in this case is 1. Therefore, the amplitude is $|1| = 1$.

2. **Period**: The period of a sine function is determined by the coefficient of $x$ inside the sine function. The formula for the period ($P$) of a sine function $y = \sin(bx)$ is $P = \frac{2\pi}{|b|}$. In this case, the coefficient of $x$ inside the sine function is $\pi$. Thus, the period is $P = \frac{2\pi}{|\pi|} = \frac{2\pi}{\pi} = 2$. Therefore, the period of the function is 2.