How do you sketch $y = 2 cos 3 (x - (\frac{π}{4}))$ $y = 2 cos 3 (x - (pi/4))$ ?

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How do you sketch $y = 2 cos 3 (x - (\frac{π}{4}))$ $y = 2 cos 3 (x - (pi/4))$ ?

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Answer 1 · 2018-06-07T06:35:22

As below.

Explanation:

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

Given $y = 2 cos 3 (x - \frac{π}{4}) = 2 cos (3 x - \frac{3 π}{4})$ $y = 2 cos 3(x - pi/4) = 2 cos (3x - (3pi)/4)$

$A m p l i t u d e = | A | = 2$ $Amplitude = |A| = 2$

$Period = \frac{2 π}{| B |} = \frac{2 π}{3}$ $"Period " = (2pi) / |B| = (2pi) / 3$

$Phase Shift = - \frac{C}{B} = \frac{\frac{3 π}{4}}{3} = \frac{π}{4}$ $"Phase Shift " = -C / B = ((3pi)/4) / 3 = pi/4$ , $\frac{π}{4}$ $color(red)(pi/4$ to the right

$Vertical Shift = D = 0$ $"Vertical Shift " = D = 0$

graph{2 cos (3x - (3pi)/4) [-10, 10, -5, 5]}

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How do you sketch $y = 2 cos 3 (x - (\frac{π}{4}))$ $y = 2 cos 3 (x - (pi/4))$ ?

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How do you sketch $y = 2 cos 3 (x - (\frac{π}{4}))$ $y = 2 cos 3 (x - (pi/4))$ ?