Given y = 5 sin(6x – pie), state the
(a) period
(b) phase shift
6x = 2 pi
x = pi/3 is the period
phase shift is pi
To determine the period and phase shift of a trigonometric function, you need to understand the general form of the function and its properties.
The general form of a trigonometric function is y = A*sin(Bx - C) + D, where:
A is the amplitude,
B is the frequency,
C is the phase shift, and
D is the vertical shift.
In the given function, y = 5*sin(6x - π), we can identify the values as follows:
Amplitude (A) = 5,
Frequency (B) = 6,
Phase shift (C) = π,
Vertical shift (D) = 0 (since it is not given).
Now, let's find the period and phase shift:
(a) The period of a sinusoidal function can be calculated using the formula T = 2π/B, where B is the frequency.
In this case, B = 6, so T = 2π/6 = π/3.
Therefore, the period is π/3.
(b) The phase shift represents a horizontal shift of the graph. It can be found using the formula C/B, where C is the phase shift and B is the frequency.
In this case, C = π and B = 6.
The phase shift is π/6.
Hence, the answers are:
(a) Period = π/3
(b) Phase shift = π/6