/*! 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 86 Use words (not an equation) to d... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Problem 86

Use words (not an equation) to describe one of the reciprocal identities.

Short Answer

Expert verified
The reciprocal identity of sine, namely the cosecant, tells us that the ratio of the length of the hypotenuse to the length of the side opposite the angle in a right triangle is actually the reciprocal of the sine of that angle.

Step by step solution

01

Select a Reciprocal Identity from Trigonometry

There are three key reciprocal identities in trigonometry tied to the three key trigonometric functions - sine, cosine, and tangent. These are cosecant (csc), secant (sec), and cotangent (cot) respectively. Each of these is the reciprocal of one of the basic functions. For the purpose of this exercise, one identity will be picked - the reciprocal identity for sine, namely cosecant.
02

Understand the Reciprocal Relationship

The reciprocal identity for sine, which is cosecant, tells us that the cosecant of an angle is actually the reciprocal of the sine of that same angle.
03

Describe the Reciprocal Identity in Words

The reciprocal identity for the sine function can be described in words as such: The value of the cosecant of an angle in a right triangle is the ratio of the length of the hypotenuse to the length of the side opposite that angle. Importantly, this is the reciprocal of the sine function, which is the ratio of the length of the side opposite the angle to the length of the hypotenuse. Therefore, the cosecant of an angle is effectively the reciprocal of the sine of that same angle.

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!

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 domain and the range of each function. $$ f(x)=\sin ^{-1}(\sin x) $$

Exercises \(127-129\) will help you prepare for the material covered in the next section. Determine the amplitude and period of \(y=10 \cos \frac{\pi}{6} x\).

\( \text { Solve: } \quad 8^{x+5}=4^{x-1}\)

Determine the domain and the range of each function. $$ f(x)=\cos ^{-1}(\cos x) $$

Assuming Earth to be a sphere of radius 4000 miles, how many miles north of the Equator is Miami, Florida, if it is \(26^{\circ}\) north from the Equator? Round your answer to the nearest mile.
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Probability and Statistics

Read Explanation

Discrete Mathematics

Read Explanation

Mechanics Maths

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.