Domanda del libro di testo
Use the given information to find tan(x + y).
sin y = - 2/3, cos x = -1/5, x in quadrant II, y in quadrant III
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Ch. 5 - Trigonometric Identities
Lial12th EditionTrigonometryISBN: 9780136552161, 9780135440780, 9780136881117, 9780135440827, 9780135924891
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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.2
For each expression in Column I, choose the expression from Column II that completes an identity.
2. csc 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 the cosecant function in terms of sine: \(\csc x = \frac{1}{\sin x}\).
Identify the expression in Column II that matches \(\frac{1}{\sin x}\) or is equivalent to it.
Verify that the chosen expression satisfies the identity by considering the domain where \(\sin x \neq 0\) to avoid division by zero.
Understand that this identity is fundamental because cosecant is the reciprocal of sine, which is a key concept in trigonometry.
Confirm that the expression from Column II correctly completes the identity \(\csc x = \frac{1}{\sin x}\).
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Concetti chiave
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Reciprocal Trigonometric Functions
The cosecant function (csc x) is the reciprocal of the sine function. This means csc x = 1/sin x, which is fundamental for rewriting or completing trigonometric identities involving csc x.
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Percorso guidato
6:04
Introduction to Trigonometric Functions
Trigonometric Identities
Trigonometric identities are equations involving trigonometric functions that hold true for all values within their domains. Recognizing and applying these identities helps simplify expressions and solve equations.
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Percorso guidato
5:32Fundamental Trigonometric Identities
Domain and Range of Trigonometric Functions
Understanding the domain and range of functions like sine and cosecant is important because csc x is undefined where sin x = 0. This knowledge ensures correct application of identities and avoids division by zero.
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Percorso guidato
4:22Domain and Range of Function Transformations
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Use the given information to find sin(x + y), cos(x - y), tan(x + y), and the quadrant of x + y.
sin x = 3/5, cos y = 24/25, x in quadrant I, y in quadrant IV
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Domanda del libro di testo
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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(-55°)
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