Problem

Given that $f(\theta)=\cos (n \theta)$ has the same period as the graph of $g(\theta)=\tan (\theta)$ the value of $n$ is

Answer

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Answer

\(\boxed{2}\)

Steps

Step 1 ：Find the value of n such that the period of \(f(\theta) = \cos(n\theta)\) is the same as the period of \(g(\theta) = \tan(\theta)\).

Step 2 ：The period of the tangent function is \(\pi\). The period of the cosine function is \(2\pi\). When there is a factor of n in the argument, the period becomes \(\frac{2\pi}{n}\).

Step 3 ：Set \(\frac{2\pi}{n}\) equal to \(\pi\) and solve for n: \(\frac{2\pi}{n} = \pi\).

Step 4 ：\(n = 2\)

Step 5 ：\(\boxed{2}\)

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