Chapter 7: Q. 1 (page 505)

Find the exact value of the expression. Express angles in radians.
$s e c^{- 1} (\frac{2}{\sqrt{3}})$

Short Answer

Expert verified

The exact value of the given expression is $\frac{π}{6}$ .

Step by step solution

Step 1. Given information.

Consider the given question,

$s e c^{- 1} (\frac{2}{\sqrt{3}})$

Assume $θ = s e c^{- 1} (\frac{2}{\sqrt{3}})$ .

As $y = \sin^{- 1} x$ means $x = \sin y$ , where,

$- \frac{π}{2} \leq θ \leq \frac{π}{2}$

Rewrite the function,

$s e c θ = \frac{2}{\sqrt{3}}$

Step 2. Use the reciprocal identity.

Using the reciprocal identity, $s e c θ = \frac{1}{\cos θ}$ ,

Then,

$\frac{1}{\cos θ} = \frac{1}{\frac{2}{\sqrt{3}}} \cos θ = \frac{\sqrt{3}}{2}$

We know $\cos \frac{π}{6} = \frac{\sqrt{3}}{2}$ and as $\frac{π}{6}$ is in the interval $0 \leq θ \leq π$ .

Then, we can say,

localid="1646501788181" $\cos θ = \cos \frac{π}{6} θ = \frac{π}{6}$

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Find the exact value of the expression. Express angles in radians.
$s e c^{- 1} (\frac{2}{\sqrt{3}})$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Use the reciprocal identity.

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Short Answer

Step by step solution

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One App. One Place for Learning.

Most popular questions from this chapter

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Find the exact value of the expression. Express angles in radians.
$s e c^{- 1} (\frac{2}{\sqrt{3}})$