Chapter 7: Q. 20 (page 450)

In Problems 13–24, find the exact value of each expression.
$\tan^{- 1} \frac{\sqrt{3}}{3}$

Short Answer

Expert verified

The exact value of $\tan^{- 1} \frac{\sqrt{3}}{3} i s \frac{π}{6}$ .

Step by step solution

Step 1. Given Information:

Given expression: $\tan^{- 1} \frac{\sqrt{3}}{3}$

We want to find the exact value of given expression.

Step 2. Solution:

The given expression can be rewritten as:

$\tan^{- 1} \frac{\sqrt{3}}{3} = x; - \frac{π}{2} < x < \frac{π}{2}$

Hence we get $\tan x = \frac{\sqrt{3}}{3}$

Since we have tan^-1 function initially, the bounds on the tan function are going to be in the interval $(- \frac{π}{2}, \frac{π}{2})$ which represents the range of tan^-1 function.

Using the unit circle, we know that in order to get $\frac{\sqrt{3}}{3}$ , x must be equal to $\frac{π}{6}$ .

Hence, we get $\tan^{- 1} \frac{\sqrt{3}}{3} = \frac{π}{6}$ .

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In Problems 13–24, find the exact value of each expression.
$\tan^{- 1} \frac{\sqrt{3}}{3}$

Short Answer

Step by step solution

Step 1. Given Information:

Step 2. Solution:

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In Problems 13–24, find the exact value of each expression.tan-133

Short Answer

Step by step solution

Step 1. Given Information:

Step 2. Solution:

One App. One Place for Learning.

Most popular questions from this chapter

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In Problems 13–24, find the exact value of each expression.
$\tan^{- 1} \frac{\sqrt{3}}{3}$