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Simplify the expression algebraically and use a graphing utility to confirm your answer graphically. $$\tan (\pi+\theta)$$

Short Answer

Expert verified
\(\tan (\pi+\theta) = \tan (\theta)\)

Step by step solution

01

Simplify the Expression Algebraically

By using the periodicity of the tangent function, which is \( \pi \), simplify the expression \(\tan (\pi+\theta)\) to be simply \( \tan (\theta) \). This means, the tangent of an angle plus \(\pi\) is equal to the tangent of the angle.
02

Confirm the Results Graphically

Use a graphing utility to plot both expressions, \( \tan (\pi+\theta) \) and \( \tan (\theta) \). According to the periodicity property, the two graphs will be identical proving that indeed \( \tan (\pi+\theta) = \tan (\theta) \).

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