Graph y=-3sin(-2x+pi/2)

Problem

y=−3*sin(−2*x+π/2)

Solution

1. Factor the coefficient of x inside the sine function to identify the horizontal shift.

y=−3*sin(−2*(x−π/4))

2. Apply the odd function property of sine, sin(−θ)=−sin(θ) to simplify the expression.

y=−3*(−sin(2*(x−π/4)))

y=3*sin(2*(x−π/4))

3. Identify the amplitude A which is the absolute value of the coefficient.

|A|=3

4. Calculate the period P using the formula P=(2*π)/|b| where b=2

P=(2*π)/2=π

5. Determine the phase shift by looking at the horizontal translation.

Phase Shift=π/4

6. Find the interval for one full cycle by setting the start at the phase shift and adding the period.

Start=π/4

End=π/4+π=(5*π)/4

7. Divide the period into four equal sub-intervals to find the key points (intercepts, maximums, and minimums).

Key points at *x=π/4,π/2,(3*π)/4,π,(5*π)/4

Final Answer

y=3*sin(2*x−π/2)

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