How do you sketch one cycle of $y = \frac{1}{2} cos (\frac{1}{3} x)$ $y=1/2cos(1/3x)$ ?

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How do you sketch one cycle of $y = \frac{1}{2} cos (\frac{1}{3} x)$ $y=1/2cos(1/3x)$ ?

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Answer 1 · 2018-07-28T04:46:11

See graph and details.

Explanation:

Cycle period for

$y = \frac{1}{2} cos (\frac{x}{3}) \in [- \frac{1}{2}, \frac{1}{2}]$ $y = 1/2 cos (x/3 ) in [ - 1/2, 1/2 ]$ is $\frac{2 π}{\frac{1}{3}} = 6 π$ $(2pi)/(1/3) = 6pi$ .

From any x = a, one cycle is $(a + 6 π)$ $( a + 6pi )$ .

Grapm for the cycle $x \in [- 3 π, 3 π]$ $x in [ - 3 pi, 3 pi ]$ , with all aspects:
graph{(y-1/2cos(x/3))(y^2-0.25)(x^2-9(pi)^2)=0[-10 10 -2 2]}

See the effect of the scale factor 1/2 on wave amplitude, from the

graph of $y = cos (\frac{x}{3})$ $y = cos ( x/3 )$ .

graph{(y-cos(x/3))=0[-10 10 -2 2]}

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How do you sketch one cycle of $y = \frac{1}{2} cos (\frac{1}{3} x)$ $y=1/2cos(1/3x)$ ?

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How do you sketch one cycle of $y = \frac{1}{2} cos (\frac{1}{3} x)$ $y=1/2cos(1/3x)$ ?