Question

What is the value of tanΘ in the unit circle below?

Answer 1

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Answer 2

From the picture, we can see the pair, bear in mind that terminal point pair is really the (x,y) pair or namely the (cosine, sine) pair, so we know what the cosine and sine are.

$\bf tan(\theta )=\cfrac{\stackrel{sine}{\quad \frac{1}{2}\quad }}{\stackrel{cosine}{\frac{\sqrt{3}}{2}}}\implies \cfrac{1}{2}\cdot \cfrac{2}{\sqrt{3}}\implies \cfrac{1}{\sqrt{3}}\implies \stackrel{\textit{rationalizing the denominator}}{\cfrac{1}{\sqrt{3}}\cdot \cfrac{\sqrt{3}}{\sqrt{3}}\implies \cfrac{\sqrt{3}}{3}}$