Skip to main content
Ch. 3 - Trigonometric Identities and Equations
Blitzer - Trigonometry 3rd Edition
Blitzer3rd EditionTrigonometryISBN: 9780137316601Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoBlitzer 3rd EditionCh. 3 - Trigonometric Identities and EquationsProblema 1
Capitolo 3, Problema 1

In Exercises 1–60, verify each identity. sin x sec x = tan x

Guida verificata passo dopo passo
1
Start by recalling the definitions of the trigonometric functions involved: \( \sin x \), \( \sec x \), and \( \tan x \).
Express \( \sec x \) in terms of \( \cos x \): \( \sec x = \frac{1}{\cos x} \).
Substitute \( \sec x \) in the left-hand side of the identity: \( \sin x \sec x = \sin x \cdot \frac{1}{\cos x} \).
Simplify the expression: \( \sin x \cdot \frac{1}{\cos x} = \frac{\sin x}{\cos x} \).
Recognize that \( \frac{\sin x}{\cos x} \) is the definition of \( \tan x \), thus verifying the identity: \( \sin x \sec x = \tan x \).

Risposta video verificata per un problema simile:

Questa soluzione video è stata consigliata dai nostri tutor come utile per risolvere questo problema.

Concetti chiave

Ecco i concetti essenziali che devi comprendere per rispondere correttamente alla domanda.

Trigonometric Identities

Trigonometric identities are equations that involve trigonometric functions and are true for all values of the variables involved. Common identities include the Pythagorean identities, reciprocal identities, and quotient identities. Understanding these identities is crucial for simplifying expressions and verifying equations in trigonometry.
Video consigliato:
Percorso guidato
5:32
Fundamental Trigonometric Identities

Reciprocal Functions

Reciprocal functions in trigonometry refer to pairs of functions where one function is the reciprocal of another. For example, the secant function (sec x) is the reciprocal of the cosine function (cos x), and the cosecant function (csc x) is the reciprocal of the sine function (sin x). Recognizing these relationships helps in transforming and simplifying trigonometric expressions.
Video consigliato:
Percorso guidato
3:23
Secant, Cosecant, & Cotangent on the Unit Circle

Quotient Identity

The quotient identity in trigonometry states that the tangent function (tan x) is the ratio of the sine function (sin x) to the cosine function (cos x). This identity can be expressed as tan x = sin x / cos x. Understanding this identity is essential for verifying equations that involve tangent, as it allows for the substitution of sine and cosine functions.
Video consigliato:
Percorso guidato
03:40
Quotients of Complex Numbers in Polar Form
Pratica correlata
Domanda del libro di testo
In Exercises 1–6, use the figures to find the exact value of each trigonometric function.

cos 2θ
922
views
Domanda del libro di testo

In Exercises 1–6, use the figures to find the exact value of each trigonometric function.

sin 2θ

679
views
Domanda del libro di testo

Use the formula for the cosine of the difference of two angles to solve Exercises 1–12. In Exercises 1–4, find the exact value of each expression. cos(45° - 30°)

1273
views