Graph y=2sin(-4x)

Problem

y=2*sin(−4*x)

Solution

1. Identify the amplitude by taking the absolute value of the coefficient of the sine function.

A=|2|=2

2. Apply the odd function property of sine, which states that sin(−θ)=−sin(θ) to rewrite the equation.

y=−2*sin(4*x)

3. Determine the period of the function using the formula P=(2*π)/|b| where b=4

P=(2*π)/4=π/2

4. Calculate the phase shift and vertical shift. Since there are no horizontal or vertical translations added to the argument or the function, both are zero.

Phase Shift=0

Vertical Shift=0

5. Find the key points for one cycle by dividing the period into four equal intervals of π/8 The points for y=−2*sin(4*x) starting at x=0 are (0,0) (π/8,−2) (π/4,0) ((3*π)/8,2) and (π/2,0)

Final Answer

y=2*sin(−4*x)=−2*sin(4*x)

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