Graph y=-6sin(x)

Problem

y=−6*sin(x)

Solution

1. Identify the parent function and its properties. The base function is y=sin(x) which has a period of 2*π an amplitude of 1 and passes through the origin (0,0)

2. Determine the amplitude of the given function. For y=a*sin(b*x) the amplitude is |a| Here, a=−6 so the amplitude is |−6|=6 This means the graph will oscillate between y=6 and y=−6

3. Identify the reflection across the x-axis. Since the coefficient a is negative (a=−6, the graph of sin(x) is reflected vertically. Instead of starting by moving upward from the origin, the graph will move downward.

4. Determine the period of the function. The coefficient of x is b=1 The period is calculated as (2*π)/|b| which results in (2*π)/1=2*π

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

• At x=0 y=−6*sin(0)=0

• At x=π/2 y=−6*sin(π/2)=−6

• At x=π y=−6*sin(π)=0

• At x=(3*π)/2 y=−6*sin((3*π)/2)=6

• At x=2*π y=−6*sin(2*π)=0

6. Plot the points and draw a smooth wave. Connect the coordinates (0,0) (π/2,−6) (π,0) ((3*π)/2,6) and (2*π,0) to complete one period of the sine wave.

Final Answer

y=−6*sin(x)

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