Question

What is the equation of a sine function with an amplitude of 2 and a period of 4

Answer 1

Answer: C

Step-by-step explanation:

For this problem, we need to know the standard form of a sine function and the meaning of each part.

Standard form: $y=asin[b(x-h)]+k$

a=amplitude

b=period

h=phase shift

k=vertical replacement/shifting

Now that we know the standard form and the components, we know that we can forget about k and plug in 0 for h. This would leave us with $y=asin[b(x)]$. We know that the amplitude is 2, therefore, a=2. To find the period, you divide 2π by the given period. $\frac{2\pi }{b} =\frac{2\pi }{4\pi } =\frac{2}{4} =\frac{1}{2}$, therefore, b=1/2.

$y=asin[b(x)]$             [plug in a=2]

$y=2sin[b(x)]$             [plug in b=1/2]

$y=2sin(\frac{1}{2}x)$

Therefore, C is the correct answer.