Draw a graph of 𝑦=2cos(2𝜋x −4)−1 Can anyone help me solve this?

Question

Amplitude = 2
Period = 1
Phase shift = $\frac{2}{π}$ $2/pi$

How to determine the period when it's not in terms of $π$ $pi$ ? How to shift the graph to the right using that phase shift value?

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Answer 1 · 2018-05-03T11:22:24

As detailed.

$y = 2 cos (2 π x - 4) - 1$ $y = 2 cos (2 pi x - 4) - 1$

Standard form of equation is $y = A cos (B x - C) + D$ $y = A cos (Bx -C) + D$

$Amplitude = | A | = 2$ $"Amplitude " = |A| = 2$

$Period = \frac{2 π}{| B |} = \frac{2 π}{2 π} = 1$ $"Period " = (2pi) / |B| = (2pi) / (2pi) = 1$

$Phase Shift = - \frac{C}{B} = \frac{4}{2 π} = \frac{2}{π}, to the right$ $"Phase Shift " = -C / B = 4 /( 2pi) = 2 / pi, " to the right"$

$Vertical Shift = D = - 1$ $"Vertical Shift " = D = -1$

graph{2 cos(2pix - 4) - 1 [-10, 10, -5, 5]}