/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 33 Find the approximate value of ea... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Problem 33

Find the approximate value of each expression. Round to four decimal places. $$\cot (-3.48)$$

Short Answer

Expert verified
The approximate value of \(\text{cot}(-3.48)\) rounded to four decimal places.

Step by step solution

01

Understand the Cotangent Function

The cotangent function, \(\text{cot}(x)\), is the reciprocal of the tangent function. That is, \(\text{cot}(x) = \frac{1}{\text{tan}(x)}\).
02

Evaluate the Tan Function

Compute \(\text{tan}(-3.48)\) using a scientific calculator to find the tangent value for the given angle in radians.
03

Calculate the Cotangent

Use the result from Step 2 and find the reciprocal: \(\text{cot}(-3.48) = \frac{1}{\text{tan}(-3.48)}\).
04

Round the Result

Round the result from Step 3 to four decimal places to get the approximate value of \(\text{cot}(-3.48)\).

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.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Understanding Cotangent
Cotangent, often abbreviated as 'cot', is a fundamental trigonometric function. Its relation to another primary function, tangent (tan), is crucial. Specifically, the cotangent of an angle is the reciprocal of its tangent, mathematically expressed as \(\text{cot}(x) = \frac{1}{\text{tan}(x)} \). This means if you know the tangent of an angle, you can easily find its cotangent by taking the reciprocal.
If you aren鈥檛 familiar, a reciprocal simply means one divided by that number. For example, the reciprocal of 5 is \(\frac{1}{5} \), and vice versa.
Understanding Tangent
The tangent function, denoted as 'tan', is another foundational trigonometric function. You can think of tangent as a ratio in a right-angled triangle. Mathematically, \(\text{tan}(x) = \frac{\text{opposite side}}{\text{adjacent side}}\). This is very useful in many fields, such as physics and engineering.
For example, if you're given an angle measure, its tangent value describes the ratio of the lengths of the side opposite to this angle to the side adjacent to it. When working with radians (not degrees), you commonly use a scientific calculator to find tangent values accurately.
Reciprocals Explained
A reciprocal of a number is what you multiply by that number to get 1. So, the reciprocal of a number \(a\) is \(\frac{1}{a} \). When it comes to trigonometric functions, working with reciprocals becomes easy, once you understand the basic principles.
For example, if you know that \(\text{tan}(-3.48) = -0.7534 \(a sample value\)\text\), then the \(\text{cot}(-3.48)\) would be \(\frac{1}{-0.7534} = -1.3276\).
Reciprocals are especially helpful in trigonometry as many functions are interrelational through them, like cotangent and tangent.
Using a Scientific Calculator
A scientific calculator is a crucial tool for solving trigonometric problems accurately. Here's how you can use it to find the tangent and cotangent of an angle in radians:
  • Step 1: Enter the angle in radians. If your calculator is in degree mode, switch it to radian mode first.
  • Step 2: Press the 'tan' button to get the tangent value of the angle.
  • Step 3: To find the cotangent, take the reciprocal of the tangent value. Many scientific calculators allow you to do this directly, often with a button that means 'reciprocal' or by using \( \frac{1}{x} \).
Scientific calculators can save you a lot of time if used correctly, ensuring your answers are precise up to the required decimal places.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Determine the period and range of each function. $$y=2 \cot (3 x+\pi)-8$$

Find the smallest positive angle in radians that is coterminal with \(-23 \pi / 6\)

Graph \(y=x+\tan x\) for \(-6 \leq x \leq 6\) and \(-10 \leq y \leq 10\) Explain your results. Average Rate of Change The average rate of change of a function on a short interval \([x, x+h]\) for a fixed value of \(h\) is a function itself. Sometimes it is a function that we can recognize by its graph. a. Graph \(y_{1}=\sin (x)\) and its average rate of change $$ y_{2}=\left(y_{1}(x+0.1)-y_{1}(x)\right) / 0.1 $$ for \(-2 \pi \leq x \leq 2 \pi .\) What familiar function does \(y_{2}\) look like? b. Repeat part (a) for \(y_{1}=\cos (x), y_{1}=e^{x}, y_{1}=\ln (x),\) and \(y_{1}=x^{2}\)

Find the exact value of each expression for the given value of \(\theta .\) Do not use a calculator. $$\sec ^{2}(2 \theta) \text { if } \theta=\pi / 6$$

Determine the period and sketch at least one cycle of the graph of each function. State the range of each function. $$y=\csc (x / 4)$$`
See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Calculus

Read Explanation

Probability and Statistics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Logic and Functions

Read Explanation

Geometry

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.