How do you graph $y = \frac{1}{2} cos π x$ $y=1/2cospix$ ?

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Answer 1 · 2017-06-06T12:29:59

Graph $cos (x)$ $cos(x)$ , then increase frequency and halve the amplitude.

Start with the graph of $y = cos (x)$ $y=cos(x)$ . The primary points required to adequately draw the graph are

$f (x) = cos (x)$ $f(x)=cos(x)$

$cos (- \frac{3 π}{2}) = 0 \Rightarrow (- \frac{3 π}{2}, 0)$ $cos(-(3pi)/2)=0 => (-(3pi)/2,0)$

$cos (- π) = - 1 \Rightarrow (- π, - 1)$ $cos(-pi)=-1 => (-pi,-1)$

$cos (- \frac{π}{2}) = 0 \Rightarrow (- \frac{π}{2}, 0)$ $cos(-(pi)/2)=0 => (-(pi)/2,0)$

$cos (0) = 1 \Rightarrow (0, 1)$ $cos(0)=1 => (0,1)$

$cos (\frac{π}{2}) = 0 \Rightarrow (\frac{π}{2}, 0)$ $cos((pi)/2)=0 => ((pi)/2,0)$

$cos (π) = - 1 \Rightarrow (π, - 1)$ $cos(pi)=-1 => (pi,-1)$

$cos (\frac{3 π}{2}) = 0 \Rightarrow (\frac{3 π}{2}, 0)$ $cos((3pi)/2)=0 => ((3pi)/2,0)$

These give the basic graph of $y = cos (x)$ $y=cos(x)$

graph{cos(x)[-5,5,-1.2,1.2]}

Next, the frequency will increase by $π$ $pi$ , or a factor of just barely over three.

graph{cos(pi*x)[-5,5,-1.2,1.2]}

Finally, cut the amplitude of the function in half.

graph{1/2 cos(pi*x)[-5,5,-1.2,1.2]}

How do you graph y=12cosπxy=1/2cospix?