Graph y=-1/2*cos(2x)

Problem

y=−1/2*cos(2*x)

Solution

1. Identify the parent function and the general form of the cosine equation, which is y=A*cos(B*x)

2. Determine the amplitude by taking the absolute value of the coefficient A

|A|=|−1/2|=1/2

3. Determine the period using the formula P=(2*π)/B where B=2

P=(2*π)/2=π

4. Identify the phase shift and vertical shift, which are both zero in this equation.

5. Account for the reflection across the x-axis because the coefficient A is negative. Instead of starting at a maximum, the graph starts at a minimum.

6. Find the key points by dividing the period into four equal intervals of π/4 The points over one period [0,π] are:

(0,−1/2)

(π/4,0)

(π/2,1/2)

((3*π)/4,0)

(π,−1/2)

7. Sketch the curve through these points, ensuring a smooth wave shape that repeats every π units.

Final Answer

y=−1/2*cos(2*x)

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