Question

What is the exact value of tan (-x/3)

Answer 1

The exact value of
`\(\tan\left((-x)/(3)\right)\)` is
`\(-\tan\left((x)/(3)\right)\).`

Step-by-step explanation:

To find the exact value of
`\(\tan\left((-x)/(3)\right)\),` we can use the periodicity property of the tangent function. The tangent function has a period of
`\(\pi\),` which means that
`\(\tan(\theta) = \tan(\theta + \pi)\)`.

Therefore,
`\(\tan\left((-x)/(3)\right)\)` is equivalent to
`\(\tan\left((-x)/(3) + \pi\)\).` Additionally, the tangent function is an odd function, so
`\(\tan(-\theta) = -\tan(\theta)\). Combining these properties, we get \(\tan\left((-x)/(3)\right) = -\tan\left((x)/(3)\right)\).`

In summary, the exact value of
`\(\tan\left((-x)/(3)\right)\) is \(-\tan\left((x)/(3)\right)\)` due to the periodicity and odd function properties of the tangent function.

Answer 2

Please see attached graph for answer

Step-by-step explanation:

Since the expression is given in terms of x

The exact value of the expression depends on th evalue of x

Please see the image below for the graph of the function for a wide range of values.