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Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 7: Q. 5 (page 504)

Find the exact value of the expression. Express angles in radians.
$c o t (c s c^{- 1} \sqrt{10})$

Short Answer

Expert verified

The exact value of the given expression is $3$ .

Step by step solution

01

Step 1. Given information.

Consider the given question,

$c o t (c s c^{- 1} \sqrt{10})$

Assume localid="1646503577094" $胃 = c s c^{- 1} (\sqrt{10})$ .

Using the inverse function,

localid="1646504501841" $c s c 胃 = \sqrt{10}$

Using the reciprocal identity,

localid="1646504121655" $\frac{1}{\sin 胃} = \sqrt{10} \sin 胃 = \frac{1}{\sqrt{10}}$

We can also say,

localid="1646504141445" $\sin 胃 = \frac{o p p o s i t e}{h y p o t e n u s e}$

02

Step 2. Use the Pythagoras theorem.

Using the Pythagoras theorem,

$a d j a c e n t = \sqrt{h y p o t e n u s e^{2} - o p p o s i t e^{2}} a d j a c e n t = \sqrt{10 - 1} a d j a c e n t = \sqrt{9} a d j a c e n t = 3$

Then, we can say,

$c o t 胃 = \frac{3}{1} 3 = \frac{a d j a c e n t}{o p p o s i t e}$

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Most popular questions from this chapter

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