/*! 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 4 In \(3-38,\) find each function ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 9: Problem 4

In \(3-38,\) find each function value to four decimal places. $$ \cos 35^{\circ} $$

Short Answer

Expert verified
\(\cos 35^{\circ} \approx 0.8192\)

Step by step solution

01

Understand the Problem

We need to find the cosine of an angle measured in degrees, specifically \(35^{\circ}\), and express it to four decimal places.
02

Use a Calculator

Input \(35^{\circ}\) into a scientific calculator set to degree mode. Make sure the calculator is in the correct mode to avoid errors.To find \(\cos 35^{\circ}\), use the cosine function button.
03

Obtain the Result

The result from the calculator for \(\cos 35^{\circ}\) should be approximately 0.8192.

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.

Cosine
The concept of cosine is fundamental in trigonometry and is one of the primary trigonometric functions, alongside sine and tangent. Cosine, often abbreviated as "cos," is used to relate the angle of a right triangle to the ratio of the length of the adjacent side over the hypotenuse. This would look like:\[\cos \theta = \frac{\text{Adjacent}}{\text{Hypotenuse}} \]Understanding this is key when working with any trigonometric problems.
  • The cosine function applies to angles measured in degrees or radians.
  • In the context of the unit circle, the cosine of an angle is the x-coordinate of the point where the terminal side of the angle intersects the circle.
  • Cosine values range from -1 to 1, where \(-1 \leq \cos \theta \leq 1\).
Recognizing when to use the cosine function can significantly simplify solving trigonometric problems.
Degree Measurement
Measuring angles in degrees is one of the most common methods used in trigonometry and geometry. A degree, denoted by the symbol "\(^\circ\)," is a measure of angle size.
  • There are 360 degrees in a circle, which provides a complete revolution or turn.
  • Degrees are often more intuitive than radians, especially for beginners or when working with familiar geometric shapes.
When calculating trigonometric values for angles measured in degrees, it is crucial to ensure that calculators and mathematical models are set to degree mode. This setting is essential for obtaining accurate results, as different settings like radians can lead to errors.Angles such as \(35^{\circ}\) are typically easy to visualize and manipulate, making degree measurement accessible and popular in educational settings.
Calculator Usage
In today鈥檚 technology-driven environment, calculators have become essential tools in mathematical calculations, especially in trigonometry.To find trigonometrical values like \(\cos 35^{\circ}\), calculators streamline the process effectively:
  • Always ensure that the calculator is in degree mode if you are working with angles measured in degrees. This can usually be checked in the settings or modes of your device.
  • Locate the cosine button鈥攐ften labeled as "cos"鈥攚hich will be used to find cosine values of angles.
  • Enter the angle given, in this case, \(35\). After typing this, hit the "cos" button to compute the value.
For \(\cos 35^{\circ}\), the calculator should display approximately 0.8192.Using calculators allows students to focus more on understanding concepts rather than manual computation, which can sometimes be complex and time-consuming.

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

In \(51-58,\) find the smallest positive value of \(\theta\) to the nearest minute. $$ \tan \theta=7.3478 $$

The terminal side of an angle in standard position intersects the unit circle at the point \((-0.8,0.6) .\) a. In what quadrant does the terminal side of the angle lie? b. Find, to the nearest degree, the smallest positive measure of the angle.

In \(3-38,\) find each function value to four decimal places. $$ \cot 165^{\circ} $$

In \(39-50,\) find the smallest positive value of \(\theta\) to the nearest degree. $$ \tan \theta=1.8808 $$

In \(3-44,\) find the exact value. $$ \sin 180^{\circ} $$
See all solutions

Recommended explanations on Math Textbooks

Logic and Functions

Read Explanation

Discrete Mathematics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Applied Mathematics

Read Explanation

Pure Maths

Read Explanation

Decision Maths

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.