Graph y=cos(x)

Problem

y=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 full cycle within the interval [0,2*π] These points occur at the quadrantal angles where the function reaches its maximum, minimum, or zero values.

3. Calculate the coordinates for these key points:

• At x=0 y=cos(0)=1

• At x=π/2 y=cos(π/2)=0

• At x=π y=cos(π)=−1

• At x=(3*π)/2 y=cos((3*π)/2)=0

• At x=2*π y=cos(2*π)=1

4. Plot these points (0,1) (π/2,0) (π,−1) ((3*π)/2,0) and (2*π,1) on a coordinate plane.

5. Sketch a smooth, continuous wave connecting these points, ensuring the curve is concave down near the maximums and concave up near the minimum.

6. Extend the pattern in both directions along the x-axis to show the periodicity of the function, as the domain is all real numbers.

Final Answer

y=cos(x)

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