Graph y=-5sin(x)

Problem

y=−5*sin(x)

Solution

1. Identify the parent function as y=sin(x) which has a period of 2*π and oscillates between −1 and 1

2. Determine the amplitude by taking the absolute value of the coefficient of the sine function, |−5|=5

3. Identify the reflection across the xaxis caused by the negative sign, meaning the graph starts at the origin and moves downward toward the minimum first.

4. Calculate the key points for one period [0,2*π] by dividing the period into four equal intervals: (0,0) (π/2,−5) (π,0) ((3*π)/2,5) and (2*π,0)

5. Sketch the smooth periodic wave passing through these key points and extending in both directions.

Final Answer

y=−5*sin(x)

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