State the period, amplitude, max/min values, range, domain, horizontal phase shift and vertical displacement. y = -2sin(360 (t +1/3)
y = -2sin(360 (t +1/3)
amplitude = 2
period = 2π/360 = π/180 radians
max value = 2
min value = -2
domain: any real number for t
range: -2 ≤ y ≤ 2
horizontal phase shift: 1/3 radians to the left
no vertical shift
beware of confusing degrees and radians.
See your other post. same question, different values.
I'm surprised you didn't learn from it, or show your own ideas.
To determine the period, amplitude, max/min values, range, domain, horizontal phase shift, and vertical displacement of the given function y = -2sin(360(t + 1/3)), we can break it down step by step.
1. Period:
The period of a sine function is given by the formula 2π/b, where b is the coefficient of the variable inside the sine function.
In this case, the coefficient inside the sine function is 360, so the period is 2π/360 = π/180.
2. Amplitude:
The amplitude of a sine function is the absolute value of the coefficient multiplying the sine function.
In this case, the coefficient is -2, so the amplitude is 2.
3. Max/Min Values:
The maximum and minimum values of the sine function are determined by the amplitude. The maximum value is equal to the amplitude, and the minimum value is the negative of the amplitude.
So, the maximum value is 2, and the minimum value is -2.
4. Range:
The range of the function represents all the possible values of y (output). Since the amplitude is 2, the range would be [-2, 2].
5. Domain:
The domain of the function represents all the possible values of t (input). Since the function is defined for all real numbers, the domain is (-∞, ∞).
6. Horizontal Phase Shift:
The horizontal phase shift represents any shift to the right or left of the standard sine function, which is y = sin(t). It is determined by the value inside the parentheses, t + 1/3 in this case.
The equation t + 1/3 = 0 can be solved to find the horizontal phase shift. Subtracting 1/3 from both sides gives t = -1/3.
So, there is a horizontal phase shift of -1/3 units to the left.
7. Vertical Displacement:
The vertical displacement represents any shift of the standard sine function up or down. It is determined by the value outside the sine function, which is -2 in this case.
Therefore, the graph is shifted downward by 2 units.
To summarize:
- Period: π/180
- Amplitude: 2
- Max Value: 2
- Min Value: -2
- Range: [-2, 2]
- Domain: (-∞, ∞)
- Horizontal Phase Shift: -1/3 units to the left
- Vertical Displacement: 2 units downward