How do you translate the graph of $y = cos (x + π) - \frac{1}{2}$ $y=cos(x+pi)-1/2$ ?

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Answer 1 · 2018-06-17T14:06:59

As below.

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

Given $y = cos (x + π) - \frac{1}{2}$ $y = cos (x + pi) - 1/2$

$A = 1, B = 1, C = - π, D = - \frac{1}{2}$ $A = 1, B = 1, C = -pi, D = -1/2$

Amplitude $= | A | = 1$ $= |A| = 1$

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

Phase Shift $= - \frac{C}{B} = - \frac{π}{1} = - π, π$ $= -C / B =- pi/1 =- pi, pi$ to the left.

Vertical Shift $= D = - \frac{1}{2}$ $= D = -1/2$

graph{cos(x + pi) - 1/2 [-10, 10, -5, 5]}

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