find the exact value. tan 5π

Explanation:

Step1: Use the periodicity of the tangent function

The tangent function (y = \tan x) has a period of (\pi), i.e., (\tan(x + n\pi)=\tan x) for any integer (n). For (x = 0) and (n = 5), we have (\tan(5\pi)=\tan(0 + 5\pi)). Since (\tan(x + n\pi)=\tan x), then (\tan(5\pi)=\tan(0)).

Step2: Evaluate (\tan(0))

We know that (\tan\theta=\frac{\sin\theta}{\cos\theta}), and when (\theta = 0), (\sin(0)=0) and (\cos(0) = 1). So (\tan(0)=\frac{\sin(0)}{\cos(0)}=\frac{0}{1}=0).

Answer:

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