On the following unit circle, $ heta$ is in radians and $ an ( heta)=\frac{-0.99}{0.1}=-9.9$.

Without a calculator, evaluate the following expressions to the nearest hundredth or as an exact ratio.
\begin{tabular}{ll}
Expression & Value \
\hline $ an (\pi+ heta)$ & $\square$ \
$ an (2 \pi+ heta)$ & $\square$
\end{tabular}

Question

On the following unit circle, $	heta$ is in radians and $	an (	heta)=\frac{-0.99}{0.1}=-9.9$.

Without a calculator, evaluate the following expressions to the nearest hundredth or as an exact ratio.
\begin{tabular}{ll} 
Expression & Value \
\hline $	an (\pi+	heta)$ & $\square$ \
$	an (2 \pi+	heta)$ & $\square$
\end{tabular}

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ Recall the periodic properties of the tangent function, specifically that $ an( heta)$ is periodic with period $\pi$. This means that $ an( heta + \pi) = an( heta)$. ‖ ‖ step 2 ⋮ Apply the periodic property to $ an(\pi + heta)$. Since $ an( heta) = -9.9$, we have $ an(\pi + heta) = an( heta) = -9.9$. ‖ ‖ step 3 ⋮ Similarly, apply the periodic property to $ an(2\pi + heta)$. Since $ an( heta)$ is periodic with period $\pi$, $ an(2\pi + heta) = an( heta) = -9.9$. ‖ ∻[question 1] Answer∻ ⚹ $ an(\pi + heta) = -9.9$ ⚹ ⚹ $ an(2\pi + heta) = -9.9$ ⚹ ∻Key Concept∻ ⚹Periodicity of the Tangent Function⚹ ∻Explanation∻ ⚹The tangent function has a period of $\pi$, which means that $ an( heta + n\pi) = an( heta)$ for any integer $n$. This property allows us to find the value of the tangent function for angles that differ by an integer multiple of $\pi$.⚹◊What is the value of $tan(2\pi + heta)$ when $ heta$ is equal to $-0.99 / 0.1 = -9.9$?⍭ Generate me a similar question◊

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