what is the period for:
$ y= 7/ (cos (1/5)x)
nevermind i figured it out.
the period is 2pi/(1/5) = 10pi or 1800º
To find the period of a function, you need to determine the interval over which the function repeats itself. In this case, the given function is $y = \frac{7}{\cos\left(\frac{1}{5}x\right)}.
The period of a function is directly related to the period of its base function. The base function in this case is the cosine function, which has a standard period of 2π (or 360 degrees).
To find the period of the given function, you need to determine how the argument of the cosine function, which is \left(\frac{1}{5}x\right), affects the period.
The argument \left(\frac{1}{5}x\right) of the cosine function controls how many cycles of the base function occur within an interval of 2π. In this case, the coefficient of x in the argument is \frac{1}{5}.
To find the period, you can set the coefficient of x in the argument equal to 2π and solve for x:
\frac{1}{5}x = 2π
To isolate x, multiply both sides of the equation by 5:
x = 2π \cdot 5
Simplifying:
x = 10π
Therefore, the period of the given function y = \frac{7}{\cos\left(\frac{1}{5}x\right)} is 10π (or 10 times the period of the base function cosine).