Textbook Question
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.
sin 300°
Ch. 5 - Trigonometric Identities
Lial12th EditionTrigonometryISBN: 9780136552161
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Table of contents
- 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
Chapter 6, Problem 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
Verified step by step guidance1
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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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
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.
Recommended video:
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.
Recommended video:
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.
Recommended video:
4:22Domain and Range of Function Transformations
Related Practice
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Textbook Question
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°)