Find the exact value of

{eq}\displaystyle{ \sec \left( \dfrac{ 2}{3}\pi \right) . } {/eq}

## Question:

Find the exact value of

{eq}\displaystyle{ \sec \left( \dfrac{ 2}{3}\pi \right) . } {/eq}

## Trigonometric Identities:

Some of the most commonly used trigonometric Identities are as mentioned below:

{eq}\displaystyle{ \sec \left( \pi - \theta \right) = - \sec \theta \\ \sec \left( 2 \pi + \theta \right) = \sec \theta \\ } {/eq}

The above-mentioned trigonometric identities are very frequently used while simplifying any trigonometric expressions.

## Answer and Explanation: 1

Using the first concept mentioned above, the given expression can be written as mentioned below:

{eq}\displaystyle{ \sec \left( \dfrac{ 2}{3}\pi \right) .= \sec \left( \pi - \dfrac{1}{3}\pi \right) = - \sec \dfrac{\pi}{3} = - 2 } {/eq}

This is the required answer.

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Chapter 22 / Lesson 11Learn what trigonometry is and what trigonometric functions are. Understand the examples of how to use each function, as well as know the instances when it is useful to use trigonometry.