/*! 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 1 Define the six trigonometric fun... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 1

Define the six trigonometric functions in terms of the sides of a right triangle.

Short Answer

Expert verified
Question: Define the six trigonometric functions in terms of the sides of a right triangle. Answer: The six trigonometric functions are defined as follows: 1. sin(胃) = Opposite / Hypotenuse 2. cos(胃) = Adjacent / Hypotenuse 3. tan(胃) = Opposite / Adjacent 4. csc(胃) = Hypotenuse / Opposite 5. sec(胃) = Hypotenuse / Adjacent 6. cot(胃) = Adjacent / Opposite

Step by step solution

01

Recall the SOHCAHTOA mnemonic

To define the six trigonometric functions, start by recalling the mnemonic SOHCAHTOA. SOHCAHTOA stands for: - Sine (sin) = Opposite / Hypotenuse - Cosine (cos) = Adjacent / Hypotenuse - Tangent (tan) = Opposite / Adjacent These functions are the primary trigonometric functions and we will use them to define the remaining three, which are the reciprocal functions.
02

Define the sine function and its reciprocal, the cosecant function

The sine function, abbreviated as sin, can be defined as the ratio of the length of the side opposite the angle (O) to the length of the hypotenuse (H). In a right triangle with an angle 胃, the sine function is: sin(胃) = O/H The reciprocal function of sine is the cosecant function (csc): csc(胃) = 1/sin(胃) = H/O
03

Define the cosine function and its reciprocal, the secant function

The cosine function, abbreviated as cos, can be defined as the ratio of the length of the side adjacent to the angle (A) to the length of the hypotenuse (H). In a right triangle with an angle 胃, the cosine function is: cos(胃) = A/H The reciprocal function of cosine is the secant function (sec): sec(胃) = 1/cos(胃) = H/A
04

Define the tangent function and its reciprocal, the cotangent function

The tangent function, abbreviated as tan, can be defined as the ratio of the length of the side opposite the angle (O) to the length of the side adjacent to the angle (A). In a right triangle with an angle 胃, the tangent function is: tan(胃) = O/A The reciprocal function of tangent is the cotangent function (cot): cot(胃) = 1/tan(胃) = A/O Now we have defined all six trigonometric functions in terms of the sides of a right triangle.

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

One function gives all six Given the following information about one trigonometric function, evaluate the other five functions. $$\cos \theta=\frac{5}{13} \text { and } 0<\theta<\pi / 2$$

One function gives all six Given the following information about one trigonometric function, evaluate the other five functions. $$\sin \theta=-\frac{4}{5} \text { and } \pi<\theta<3 \pi / 2$$

Right-triangle relationships Use a right triangle to simplify the given expressions. Assume \(x>0.\) $$\cot \left(\tan ^{-1} 2 x\right)$$

Find all the inverses associated with the following functions and state their domains. $$f(x)=2 x /(x+2)$$

Modify the proof outlined in Exercise 84 and use property E2 for exponents to prove that \(\log _{b}(x / y)=\log _{b} x-\log _{b} y\)
See all solutions

Recommended explanations on Math Textbooks

Applied Mathematics

Read Explanation

Probability and Statistics

Read Explanation

Logic and Functions

Read Explanation

Discrete Mathematics

Read Explanation

Calculus

Read Explanation

Pure 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.