Graph y=-6cos(x)

Problem

y=−6*cos(x)

Solution

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

2. Determine the amplitude of the given function. The coefficient in front of the cosine function is −6 The amplitude is the absolute value of this coefficient.

Amplitude=|−6|=6

3. Identify the vertical reflection. Because the coefficient is negative, the graph is reflected across the xaxis. Instead of starting at a maximum, the graph starts at a minimum point (0,−6)

4. Determine the period. The coefficient of x is 1 so the period remains the standard period for cosine.

Period=2*π

5. Find key points for one cycle by dividing the period into four equal intervals of π/2

Point 1: *(0,−6)

Point 2: *(π/2,0)

Point 3: *(π,6)

Point 4: *((3*π)/2,0)

Point 5: *(2*π,−6)

6. Sketch the graph by plotting these key points and connecting them with a smooth, continuous wave.

Final Answer

y=−6*cos(x)

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