Consider the following.
f\(x\) = 5tan(1/3 x + pi/2)
The period of the function above is ...
Consider the following.
newskills15
Solve for BC (the the nearest hundredth).
5tan((1/3)x + π/2)
= 5tan [(1/3)(x + 3π/2)]
period = 2π/(1/3) = 6π
onsider the following.
newskills15
Solve for BC (the the nearest hundredth).
To find the period of the function \(f(x) = 5\tan(\frac{1}{3}x + \frac{\pi}{2})\), we can use the properties of the tangent function.
The general form of the tangent function is \(y = \tan(ax + b)\), where \(a\) and \(b\) are constants.
The period of the general form of the tangent function is given by \(T = \frac{\pi}{a}\). In this case, \(a = \frac{1}{3}\), so the period \(T\) of the function \(f(x) = 5\tan(\frac{1}{3}x + \frac{\pi}{2})\) is:
\[T = \frac{\pi}{\frac{1}{3}}\]
\[T = \frac{3\pi}{1}\]
\[T = 3\pi\]
Therefore, the period of the function \(f(x) = 5\tan(\frac{1}{3}x + \frac{\pi}{2})\) is \(3\pi\).