Given that the formula is y=-9cos12x+9

What is k in radian?

Where and what is k ?

To determine the value of k in radians in the given formula y = -9cos(12x) + 9, we need to compare it to the standard cosine function, which is y = cos(x).

In the standard cosine function, the amplitude (A) is 1, and the period (T) is 2π. The general equation for the cosine function is y = A*cos(Bx + C) + D, where B represents the coefficient of x.

Comparing the given equation y = -9cos(12x) + 9 to y = cos(x), we can see that the coefficient of x in the given equation is 12, which means B = 12.

The value of B in the cosine function formula is directly related to the period (T) of the function. The period is given by T = (2π)/B. Therefore, substituting B = 12 in the equation, we determine the period as:

T = (2π)/12
T = π/6

Since the period is π/6, the function completes one full cycle within that interval. This means that the value of k represents the fraction of a full cycle completed by the function.

To find k in radians, we can write the equation:

k = (2π)/T
k = (2π)/(π/6)
k = 2π*(6/π)
k = 12

Therefore, the value of k in radians in the given equation is 12.