Find the Exact Value of the Expression $\tan \left( \cos ^ { - 1 } \frac { 1 } { 3 } \right)$

question 170

Multiple Choice

Find the exact value of the expression.
- $\tan \left( \cos ^ { - 1 } \frac { 1 } { 3 } \right)$

• A) \(2 \sqrt { 2 }\)
• B) \(2 \sqrt { 3 }\)
• C) \(\frac { 2 \sqrt { 2 } } { 3 }\)
• D) \(- 2 \sqrt { 3 }\)

---

Definitions:

Marco Polo

An Italian merchant, explorer, and writer who traveled through Asia along the Silk Road to China, where he spent over two decades in the 13th century.

Yuan Dynasty

The dynasty established by Kublai Khan in China that ruled from 1271 to 1368, characterized by significant cultural contributions and the integration of Mongol and Chinese elements.

Zhu Yuanzhong

Also known as Hongwu Emperor, founder of the Ming Dynasty in China, ruling from 1368 to 1398, noted for his successful expelling of the Mongols and significant agricultural, military, and administrative reforms.

Ming Dynasty

A major Chinese dynasty that ruled from 1368 to 1644, known for its trade expansion to the outside world and cultural achievements such as porcelain, literature, and the building of the Great Wall.