Chapter 7: Q 50. (page 457)

In Problems 45–56, use a calculator to find the value of each expression rounded to two decimal places.
$c o t^{- 1} (- \frac{1}{2})$

Short Answer

Expert verified

The value of the given expression in two decimal places is $- 1.11$

Step by step solution

Step 1. Write the given information.

$c o t^{- 1} (- \frac{1}{2})$

Step 2. Rewrite the given expression.

The given expression can be rewritten as:

$c o t^{- 1} (- \frac{1}{2}) = x$

We apply the $c o t$ function on both sides so we get:

$c o t (c o t^{- 1} (- \frac{1}{2})) = c o t x c o t x = - \frac{1}{2}$

Step 3. Use the trigonometric identity.

We know that

$c o t x = \frac{1}{\tan x} \frac{1}{\tan x} = - \frac{1}{2} \tan x = - 2$

We apply the $\tan^{- 1}$ function on both sides we get:

$\tan^{- 1} (\tan x) = \tan^{- 1} (- 2) x = \tan^{- 1} (- 2)$

Step 4. Use the calculator to find the value.

$x = - 1.11 c o t^{- 1} (- \frac{1}{2}) = - 1.11$

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

In Problems 45–56, use a calculator to find the value of each expression rounded to two decimal places.
$c o t^{- 1} (- \frac{1}{2})$

Short Answer

Step by step solution

Step 1. Write the given information.

Step 2. Rewrite the given expression.

Step 3. Use the trigonometric identity.

Step 4. Use the calculator to find the value.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Statistics

Calculus

Logic and Functions

Geometry

Mechanics Maths

Study anywhere. Anytime. Across all devices.

In Problems 45–56, use a calculator to find the value of each expression rounded to two decimal places.cot-1-12

Short Answer

Step by step solution

Step 1. Write the given information.

Step 2. Rewrite the given expression.

Step 3. Use the trigonometric identity.

Step 4. Use the calculator to find the value.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Statistics

Calculus

Logic and Functions

Geometry

Mechanics Maths

Study anywhere. Anytime. Across all devices.

In Problems 45–56, use a calculator to find the value of each expression rounded to two decimal places.
$c o t^{- 1} (- \frac{1}{2})$