How do you use transformation to graph the cosine function and determine the amplitude and period of $y = 2 cos (\frac{1}{3} x)$ $y=2cos(1/3x)$ ?

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Answer 1 · 2018-04-08T05:41:41

Amplitude: $2$ $2$ Period: $6 π$ $6pi$

For a cosine function in the form

$y = A cos (b x),$ $y=Acos(bx),$ the amplitude is given by $| A |$ $|A|$ and the period by $P = \frac{2 π}{b}$ $P=(2pi)/b$

Here, $A = 2,$ $A=2,$ so the amplitude is $| 2 | = 2$ $|2|=2$

$b = \frac{1}{3}, P = \frac{2 π}{\frac{1}{3}} = 2 π \cdot 3 = 6 π$ $b=1/3, P=(2pi)/(1/3)=2pi*3=6pi$

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