Graph 2sin(x)

Problem

y=2*sin(x)

Solution

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

2. Determine the amplitude of the given function. The coefficient 2 in front of the sine function represents a vertical stretch. The amplitude is |2|=2

3. Determine the period of the function. Since the coefficient of x is 1 the period remains 2*π

4. Identify key points for one full cycle (0≤x≤2*π.

• At x=0 y=2*sin(0)=0

• At x=π/2 y=2*sin(π/2)=2*(1)=2

• At x=π y=2*sin(π)=0

• At x=(3*π)/2 y=2*sin((3*π)/2)=2*(−1)=−2

• At x=2*π y=2*sin(2*π)=0

5. Plot the points and draw a smooth sinusoidal curve. The graph oscillates between a maximum of 2 and a minimum of −2

Final Answer

y=2*sin(x)

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