Graph y=sin(-2x)

Problem

y=sin(−2*x)

Solution

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

2. Apply the odd function property of the sine function. Since sin(−θ)=−sin(θ) the equation y=sin(−2*x) can be rewritten as y=−sin(2*x)

3. Determine the amplitude. The coefficient of the sine function is −1 so the amplitude is |−1|=1 This means the graph oscillates between y=1 and y=−1

4. Calculate the period. The coefficient of x is B=2 The period P is calculated using the formula P=(2*π)/|B|

P=(2*π)/2=π

5. Identify the phase shift and vertical shift. There are no horizontal or vertical translations, so the phase shift is 0 and the vertical shift is 0

6. Find key points for one period [0,π] Divide the period into four equal intervals of length π/4

• At x=0 y=−sin(0)=0

• At x=π/4 y=−sin(π/2)=−1

• At x=π/2 y=−sin(π)=0

• At x=(3*π)/4 y=−sin((3*π)/2)=1

• At x=π y=−sin(2*π)=0

7. Sketch the graph by plotting these points and drawing a smooth wave. The graph is a sine wave reflected across the x-axis with a period of π

Final Answer

y=−sin(2*x)

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