find the period, amplitude and phase angle of the function 2y=3 sin(1/2x-60)
recall that for the function
y = a sin(b(x-c))
you have
amplitude = a
period = 2π/b
phase shift = c (to the right)
So, your function is y = 3/2 sin(1/2 (x-120))
giving you
amplitude = 3/2
period = 2π/(1/2) = 4π
phase shift = 120
Oh, finding the period, amplitude, and phase angle, huh? Let's have some mathematical fun, shall we?
First, let's look at the expression 1/2x - 60. It represents the phase angle, which tells us how the graph of the function is shifted horizontally.
Now, the general form of a sine function is y = A sin(Bx - C) + D, where A is the amplitude, B is the coefficient of x, C is the phase angle, and D is a vertical shift if any.
In this case, we have 2y = 3 sin(1/2x - 60). To find the amplitude, we need to divide the coefficient of the sine function (which is 3) by 2. So, the amplitude is 3/2.
To find the period, we need to look at the coefficient of x in the argument of the sine function (which is 1/2). The formula for the period of a sine function is 2π/B, where B is the coefficient of x. So, in this case, the period is 2π/(1/2), which simplifies to 4π.
As for the phase angle, we have 1/2x - 60. Since the phase angle is equal to -C (where C is the coefficient of x in the argument of the sine function), the phase angle in this case is -(-60), which becomes 60.
So, to summarize: the amplitude is 3/2, the period is 4π, and the phase angle is 60 degrees. Now go out there and trig it up with confidence!
To find the period, amplitude, and phase angle of the function 2y = 3 sin(1/2x - 60), we can use the standard form of a sinusoidal function: y = A sin(B(x - C)) + D.
Step 1: Compare the given equation to the standard form equation.
- In the given equation, we have A = 3, B = 1/2, C = 60, and D = 0.
Step 2: Period (T)
- The period of a sinusoidal function is given by T = 2π/B.
- Substituting the value of B into the formula, we get T = 2π/(1/2) = 4π.
Step 3: Amplitude (A)
- The amplitude of a sinusoidal function is given by A.
- In this case, the amplitude is A = 3.
Step 4: Phase Angle (C)
- The phase angle of a sinusoidal function is given by C.
- In this case, the phase angle is C = 60.
Therefore, the period is 4π, the amplitude is 3, and the phase angle is 60.
To find the period, amplitude, and phase angle of the function 2y = 3 sin(1/2x - 60), we need to understand the general form of a sine function.
The general form of a sine function is given by y = A sin(Bx + C), where:
- A represents the amplitude,
- B represents the reciprocal of the period, and
- C represents the phase angle.
Comparing this with our given function, 2y = 3 sin(1/2x - 60), we can conclude that:
Amplitude (A) = 3/2
The amplitude (A) is determined by the coefficient of the sine function, which is 3/2 in this case. Thus, the amplitude is 3/2.
Period (P) = |2π / B|
The period (P) is determined by the coefficient of x, which is 1/2. The reciprocal of 1/2 gives us 2. Therefore, the period is |2π / 2| = π.
Phase Angle (θ) = -C/B
The phase angle (θ) is determined mainly by the term inside the sine function. In this case, the phase angle is -(-60)/(1/2) = 120.
In summary, the period is π, the amplitude is 3/2, and the phase angle is 120.