Question

Which function has a period of 4π?

y = one-half sine (one-half x)
y = sine (one-fourth x)
y = 2sin(2x)
y = 4sin(x)

Answer 1

Answer:

The answer is a

Step-by-step explanation:

based on the equation, period=2pi/b, you can just plug in the values for the equation on each option, b being the constant in front of x.

Answer 2

The time period of first option is $4 \pi$.

Thus, first option is correct.

Compare given option from  $y=asin(wx)$

Where w is frequency.

First option is,  $y=\frac{1}{2} sin(\frac{1}{2}x )$

After comparing,  We get   $w=\frac{1}{2}$

As we know that,   Time period $T=\frac{2\pi}{w}$

              $T=\frac{2\pi}{1/2}=4\pi$

Hence, function  $y=\frac{1}{2} sin(\frac{1}{2}x )$ has period of $4\pi$.

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