Did you know?
Did you know that when analyzing a trigonometric function like y = -2 sin(360°(t+1)/3), there are multiple key components to consider?
1. Period: The period of the function is the distance or interval between two consecutive cycles or wave-like patterns. In this case, the period is 3 units because it's the denominator of (t+1)/3.
2. Amplitude: The amplitude represents the maximum displacement or distance from the mean or equilibrium position. In this function, the amplitude is 2 since it is multiplied by sin.
3. Max/Min value: The maximum and minimum values of the function occur at the top-most and bottom-most points of the wave. As the coefficient of sin is negative in this case, it means that the maximum value would be -2 and the minimum value would be +2.
4. Range: The range of a function refers to the set of all possible output values or y-values. In this case, the range would be [-2, 2], as the function oscillates between -2 and 2.
5. Domain: The domain of a function represents the set of all possible input values or x-values. As the function involves time (t) and does not have any restrictions mentioned, the domain could be all real numbers unless otherwise specified.
6. Horizontal Phase Shift: A horizontal phase shift represents the horizontal displacement or shift of the entire function. In this case, the function is shifted to the left by 1 unit, as indicated by the "+1" in (t+1).
7. Vertical Displacement: A vertical displacement represents the vertical shift or movement of the entire function. In this case, there is no vertical displacement mentioned, so the function retains its mean or equilibrium position.
These aspects can provide a starting point for understanding and analyzing the given function in terms of its behavior, values, and properties.
