/*! 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 68 Find the function value. Round t... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 6: Problem 68

Find the function value. Round to four decimal places. $$\sec 35.28^{\circ}$$

Short Answer

Expert verified
1.2249

Step by step solution

01

Understand the Secant Function

The secant function, \(\text{sec}(x)\), is the reciprocal of the cosine function, \(\text{cos}(x)\). This means that \(\text{sec}(x) = \frac{1}{\text{cos}(x)}\).
02

Calculate Cosine of the Angle

First, find the cosine of the given angle. Using a calculator in degree mode, find \( \text{cos}(35.28^{\circ}) \). This gives us approximately \( \text{cos}(35.28^{\circ}) \approx 0.8163 \).
03

Take the Reciprocal

To find the secant, take the reciprocal of the cosine value: \( \text{sec}(35.28^{\circ}) = \frac{1}{ \text{cos}(35.28^{\circ})} \). This gives us \( \text{sec}(35.28^{\circ}) \approx \frac{1}{0.8163} \approx 1.2249 \).

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.

Secant Function
The secant function, denoted as \( \text{sec}(x) \), is a fundamental trigonometric function. It is defined as the reciprocal of the cosine function. This means that \( \text{sec}(x) = \frac{1}{\text{cos}(x)} \).

If you know the cosine of an angle, you can easily find the secant by taking its reciprocal. Here's a quick summary:
  • First, determine \( \text{cos}(x) \).
  • Then, take the reciprocal to get \( \text{sec}(x) \), which is \( \frac{1}{\text{cos}(x)} \).
Understanding this relationship is crucial for solving problems related to the secant function!
Cosine Function
The cosine function, \( \text{cos}(x) \), is one of the primary trigonometric functions. It describes the ratio of the adjacent side to the hypotenuse in a right triangle.

When you are given an angle, you can calculate its cosine using a calculator set to the degree mode. For example, for an angle of \( 35.28^{\circ} \),

\[ \text{cos}(35.28^{\circ}) \approx 0.8163 \].

This value helps us in calculating other related trigonometric functions. Knowing how to find the cosine is a fundamental step in solving many trigonometric problems.
Reciprocal
A reciprocal of a number is simply 1 divided by that number. In mathematical terms, the reciprocal of \( x \) is \( \frac{1}{x} \). This concept is widely used in trigonometry.

For example, if you have the cosine of an angle \[ \text{cos}(x) \approx 0.8163 \], to find the secant:
  • Take the reciprocal of the cosine value.
This means \[ \text{sec}(35.28^{\circ}) = \frac{1}{0.8163} \approx 1.2249 \].

Grasping the idea of reciprocals can simplify many trigonometric calculations and make solving problems much easier!

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

For angles of the following measures, state in which quadrant the terminal side lies. It helps to sketch the angle in standard position. $$187^{\circ}$$

Find all numbers \(x\) that satisfy the following. Check using a graphing calculator. a) \(\sin x=1\) b) \(\cos x=-1\) c) \(\sin x=0\)

Use a graphing calculator to graph the function. $$y=4 \cos 2 x-2 \sin x$$

Height of a Kite. For a science fair project, a group of students tested different materials used to construct kites. Their instructor provided an instrument that accurately measures the angle of elevation. In one of the tests, the angle of elevation was \(63.4^{\circ}\) with \(670 \mathrm{ft}\) of string out. Assuming the string was taut, how high was the kite?

Two pulleys, \(50 \mathrm{cm}\) and \(30 \mathrm{cm}\) in diameter, respectively, are connected by a belt. The larger pulley makes 12 revolutions per minute. Find the angular speed of the smaller pulley, in radians per second. (IMAGE CAN NOT COPY)
See all solutions

Recommended explanations on Math Textbooks

Discrete Mathematics

Read Explanation

Logic and Functions

Read Explanation

Decision Maths

Read Explanation

Geometry

Read Explanation

Mechanics Maths

Read Explanation

Statistics

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.