Domanda del libro di testo
Use identities to write each expression in terms of sin θ and cos θ, and then simplify so that no quotients appear and all functions are of θ only.
csc θ - sin θ
899
views
Ch. 5 - Trigonometric Identities
Lial12th EditionTrigonometryISBN: 9780136552161, 9780135440780, 9780136881117, 9780135440827, 9780135924891
Non è quello che usi tu?Cambia libro di testoScegli un libro di testo diverso
TOC.tableOfContents
- Ch. R - Algebra Review381
- Ch. 1 - Trigonometric Functions188
- Ch. 2 - Acute Angles and Right Triangles168
- Ch. 3 - Radian Measure and The Unit Circle155
- Ch. 4 - Graphs of the Circular Functions100
- Ch. 5 - Trigonometric Identities238
- Ch. 6 - Inverse Circular Functions and Trigonometric Equations158
- Ch. 7 - Applications of Trigonometry and Vectors148
- Ch. 8 - Complex Numbers, Polar Equations, and Parametric Equations15
Lial12th EditionTrigonometryISBN: 9780136552161, 9780135440780, 9780136881117, 9780135440827, 9780135924891Non è quello che usi tu?Cambia libro di testo
Capitolo 6, Problema 5.RE.4
For each expression in Column I, choose the expression from Column II that completes an identity.
4. cot x = ____
II
A. sin ^2 x/cos ^2 x
B.1/(sec ^2 x)
C. sin (-x)
D. csc ^2 x-cot ^2 x + sin ^2 x
E. tan x
Guida verificata passo dopo passo1
Recall the definition of cotangent in terms of sine and cosine functions: \(\cot x = \frac{\cos x}{\sin x}\).
Identify the reciprocal relationship between cotangent and tangent: \(\cot x = \frac{1}{\tan x}\).
Recognize that cotangent can also be expressed using cosecant and cosine: \(\cot x = \csc x \cos x\).
Review the expressions given in Column II and compare them with these equivalent forms of \(\cot x\).
Select the expression from Column II that matches one of these equivalent forms to complete the identity.
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.
Definition of Cotangent
Cotangent (cot x) is a fundamental trigonometric function defined as the ratio of the adjacent side to the opposite side in a right triangle. It can also be expressed as the reciprocal of the tangent function, i.e., cot x = 1/tan x.
Video consigliato:
Percorso guidato
5:37
Introduction to Cotangent Graph
Reciprocal Identities
Reciprocal identities relate trigonometric functions to their reciprocals. For example, cot x is the reciprocal of tan x, and sec x is the reciprocal of cos x. Understanding these identities helps in transforming and simplifying expressions.
Video consigliato:
Percorso guidato
6:25Pythagorean Identities
Relationship Between Cotangent and Sine/Cosine
Cotangent can also be expressed as the ratio of cosine to sine, cot x = cos x / sin x. This relationship is useful for converting between different trigonometric functions and proving identities.
Video consigliato:
Percorso guidato
5:05Amplitude and Reflection of Sine and Cosine
Pratica correlata
Domanda del libro di testo
Find values of the sine and cosine functions for each angle measure.
2y, given sec y = -5/3, sin y > 0
689
views
Domanda del libro di testo
Use the given information to cos(x - y).
cos x = 2/9, sin y = -1/2, x in quadrant IV, y in quadrant III
821
views
Domanda del libro di testo
For each expression in Column I, use an identity to choose an expression from Column II with the same value. Choices may be used once, more than once, or not at all.
cos 75°
726
views
Domanda del libro di testo
Work each problem.
Given tan x = -5⁄4, where π/2< x < π, use the trigonometric identities to find cot x, csc x and sec x.
808
views
Domanda del libro di testo
Graph each expression and use the graph to make a conjecture, predicting what might be an identity. Then verify your conjecture algebraically.
csc x - cot x
721
views