Graph y=cos(-x)

Problem

y=cos(−x)

Solution

1. Identify the parity of the cosine function. The cosine function is an even function, which means it satisfies the property cos(−θ)=cos(θ)

2. Simplify the expression using the even function property.

cos(−x)=cos(x)

3. Determine the key characteristics of the parent function y=cos(x) The function has an amplitude of 1 a period of 2*π and a midline at y=0

4. Identify key points for one period [0,2*π] The points are (0,1) (π/2,0) (π,−1) ((3*π)/2,0) and (2*π,1)

5. Sketch the graph by plotting these points and connecting them with a smooth, wave-like curve. Since cos(−x)=cos(x) the graph is identical to the standard cosine curve, which is symmetric about the yaxis.

Final Answer

y=cos(x)

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