What is the phase shift of y=6cos(6x+pi/2)?
y=6cos(6x+pi/2)
y = 6 cos 6(x + π/12)
y = 6cos 6x has been shifted π/12 to the left.
To find the phase shift of the function y = 6cos(6x + π/2), we need to analyze the argument of the cosine function, which is 6x + π/2.
The general form of a cosine function is y = A*cos(Bx + C), where A represents the amplitude, B represents the frequency, and C represents the phase shift.
We can see that in the given function, B is 6, which means the frequency is 6. This tells us that the graph will complete 6 cycles within an interval of 2π (one full revolution).
To determine the phase shift, we can compare the argument 6x + π/2 to the standard form Bx + C. We want to find the value of C that makes these two expressions equivalent.
Comparing the given argument 6x + π/2 to Bx + C, we can see that when Bx + C equals 6x + π/2, the two expressions are the same. This implies that B = 6 and C = π/2, which is the phase shift of the function.
So, the phase shift of y = 6cos(6x + π/2) is π/2.
Explanation of how to determine the phase shift:
1. Examine the argument of the cosine function.
2. Compare it to the standard form Bx + C.
3. Equate the coefficients of x in both expressions.
4. Solve for the phase shift value (C) that makes the expressions equivalent.