Graph f(x)=cos(x)

Problem

ƒ(x)=cos(x)

Solution

1. Identify the parent function as the cosine function, which is a periodic trigonometric function with a period of 2*π and an amplitude of 1

2. Determine the key points for one period [0,2*π] by evaluating the function at standard quadrantal angles.

3. Evaluate the function at x=0 to find ƒ(0)=cos(0)=1

4. Evaluate the function at x=π/2 to find ƒ(π/2)=cos(π/2)=0

5. Evaluate the function at x=π to find ƒ(π)=cos(π)=−1

6. Evaluate the function at x=(3*π)/2 to find ƒ((3*π)/2)=cos((3*π)/2)=0

7. Evaluate the function at x=2*π to find ƒ*(2*π)=cos(2*π)=1

8. Sketch the curve by connecting these points (0,1) (π/2,0) (π,−1) ((3*π)/2,0) and (2*π,1) with a smooth, wave-like shape and extend the pattern in both directions.

Final Answer

ƒ(x)=cos(x)

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