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What is the value of
tan((pi)/(3)) ?
Choose 1 answer:
(A)
(1)/(2)
(B)
(sqrt3)/(3)
(c)
(sqrt3)/(2)
(D)
sqrt3

What is the value of $\tan \left(\frac{\pi}{3}\right)$ ? $\newline$ Choose $1$ answer: $\newline$ (A) $\frac{1}{2}$ $\newline$ (B) $\frac{\sqrt{3}}{3}$ $\newline$ (C) $\frac{\sqrt{3}}{2}$ $\newline$ (D) $\sqrt{3}$

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Mean, median, mode, and range: find the missing number

Full solution

Q. What is the value of

\tan \left(\frac{\pi}{3}\right)

?

\newline

Choose

1

answer:

\newline

(A)

\frac{1}{2}

\newline

(B)

\frac{\sqrt{3}}{3}

\newline

(C)

\frac{\sqrt{3}}{2}

\newline

(D)

\sqrt{3}

Recalling the unit circle: To find the value of $\tan\left(\frac{\pi}{3}\right)$ , we need to recall the unit circle or the special triangles. The angle $\frac{\pi}{3}$ radians corresponds to $60$ degrees.
Using a $30$ $-60$ $-90$ triangle: In a $30$ $-60$ $-90$ right triangle, the sides are in the ratio $1 : \sqrt{3} : 2$ . The shortest side (opposite the $30$ -degree angle) is $1$ , the side opposite the $60$ -degree angle (which is $\tan\left(\frac{\pi}{3}\right)$ ) is $\sqrt{3}$ , and the hypotenuse (opposite the $90$ -degree angle) is $2$ .
Finding the tangent of $\frac{\pi}{3}$ : The tangent of an angle in a right triangle is the ratio of the length of the opposite side to the length of the adjacent side. So, $\tan\left(\frac{\pi}{3}\right) = \frac{\text{length of opposite side to } 60^\circ}{\text{length of adjacent side to } 60^\circ}$ .
Applying the side ratios: Using the side ratios for a $30$ $-60$ $-90$ triangle, $\tan\left(\frac{\pi}{3}\right) = \frac{\sqrt{3}}{1} = \sqrt{3}$ .

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