Math - Find the amplitude, period, phase shift - y=cosPi/2 (x+1/3)
To find the amplitude, period, and phase shift of the given function y = cos(π/2)(x + 1/3), let's break down the equation step by step.
1. Amplitude (A): The amplitude of a cosine function is the absolute value of the coefficient in front of the cosine function. In this case, the coefficient is 1. So, the amplitude is |1| = 1.
2. Period (P): The period of a cosine function can be obtained by the following formula: P = 2π / b, where b is the coefficient of x within the cosine function. In this equation, the coefficient in front of x is π/2 (or divided by 2), so the coefficient of x is 1/2. Thus, the period is P = 2π / (1/2) = 4π.
3. Phase Shift (C): The phase shift of a cosine function can be determined by isolating the x value within the parentheses of the function. In this case, x + 1/3 = 0, so x = -1/3. Therefore, the phase shift is -1/3 units to the left.
Summary:
Amplitude (A) = 1
Period (P) = 4π
Phase Shift (C) = -1/3
Note: The phase shift is equivalent to the horizontal displacement of the graph. The negative phase shift value indicates a shift to the left, while a positive value would be a shift to the right.