- #1
lucifer_x
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Homework Statement
Write an equation of a sine function with a amp=(2/3) , Period = 4╥ and a phase shift of ╥/2.
in radians
Homework Equations
The Attempt at a Solution
i got
y = 2/3 cos (2...
lucifer_x said:Homework Statement
Write an equation of a sine function with a amp=(2/3) , Period = 4╥ and a phase shift of ╥/2.
in radians
Homework Equations
The Attempt at a Solution
i got
y = 2/3 cos (2...
lucifer_x said:so would the answer be
y = - 2/3 sin ( 2Θ + π )
and
y = 2/3 sin ( 2Θ + π )
??
To solve a radian equation with given values for amplitude, period, and shift, you can use the formula y = A*sin(B(x-C)) + D, where A is the amplitude, B is the frequency (calculated as 2π/period), C is the horizontal shift, and D is the vertical shift. Simply plug in the given values and solve for x.
The amplitude in a radian equation represents half the distance between the maximum and minimum values. It is also equal to the absolute value of the vertical shift (D) in the formula y = A*sin(B(x-C)) + D.
Yes, a radian equation can have multiple solutions. This is because the sine function is a periodic function, meaning it repeats itself over a given interval. In this case, the interval is the period (4π), so there can be multiple values of x that satisfy the equation.
To graph a radian equation with given values for amplitude, period, and shift, plot the key points (maximum, minimum, and x-intercepts) by plugging in values of x and solving for y using the formula y = A*sin(B(x-C)) + D. Then, use these points to sketch the graph of the equation, making sure to show the periodic nature of the function.
Yes, a radian equation can have a negative amplitude. This simply means that the graph will be reflected over the x-axis. The absolute value of the amplitude still represents the distance between the maximum and minimum values, but the negative sign indicates a reflection of the graph.