Chapter 7: Q. 6 (page 505)

Find the exact value of the expression. Express angles in radians.
$s e c (\cos^{- 1} (- \frac{3}{4}))$

Short Answer

Expert verified

The exact value of the given expression is $- \frac{4}{3}$ .

Step by step solution

Step 1. Given information.

Consider the given question,

$s e c (\cos^{- 1} (- \frac{3}{4}))$

Assume $θ = \cos^{- 1} (- \frac{3}{4})$ .

Using the inverse function,

$\cos θ = - \frac{3}{4}$

We can also say,

$\sin θ = \frac{o p p o s i t e}{h y p o t e n u s e}$

Step 2. Rewrite the expression.

On rewriting the expression,

$θ = \cos^{- 1} (\frac{- 3}{4}) s e c θ = s e c (\cos^{- 1} (\frac{- 3}{4}))$

Then,

$s e c θ = \frac{1}{\cos θ} = \frac{1}{(\frac{- 3}{4})} = (- \frac{4}{3})$

Therefore, $s e c (\cos^{- 1} (- \frac{3}{4})) = - \frac{4}{3}$ .

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Find the exact value of the expression. Express angles in radians.
$s e c (\cos^{- 1} (- \frac{3}{4}))$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Rewrite the expression.

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Find the exact value of the expression. Express angles in radians.
$s e c (\cos^{- 1} (- \frac{3}{4}))$