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# How do you sketch y = 2 cos 3 (x - (pi/4))?

Jun 7, 2018

As below.

#### Explanation:

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

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

$A m p l i t u \mathrm{de} = | A | = 2$

$\text{Period } = \frac{2 \pi}{|} B | = \frac{2 \pi}{3}$

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

$\text{Vertical Shift } = D = 0$

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

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