Graph y=-cos(x)

Problem

y=−cos(x)

Solution

1. Identify the parent function and its key characteristics. The parent function is y=cos(x) which has a period of 2*π an amplitude of 1 and starts at a maximum point (0,1)

2. Apply the transformation for the negative sign. The negative sign in front of the function represents a reflection across the xaxis.

3. Determine the key points for one period [0,2*π] By reflecting the standard cosine values, the new coordinates are:

(0,−1)

(π/2,0)

(π,1)

((3*π)/2,0)

(2*π,−1)

4. Sketch the curve by plotting these points and connecting them with a smooth, wave-like shape. The graph oscillates between y=−1 and y=1

Final Answer

y=−cos(x)

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