Textbook Question
Find the angle of least positive measure that is coterminal with each angle. 792°
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Ch. 1 - Trigonometric Functions
Lial12th EditionTrigonometryISBN: 9780136552161, 9780135440780, 9780136881117, 9780135440827, 9780135924891
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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
Lial12th EditionTrigonometryISBN: 9780136552161, 9780135440780, 9780136881117, 9780135440827, 9780135924891Not the one you use?Change textbook
Chapter 2, Problem 5
CONCEPT PREVIEW Determine whether each statement is possible or impossible. sin θ = 1/2 , csc θ = 2
Verified step by step guidance1
Recall the definitions of sine and cosecant functions: \(\sin \theta = \frac{\text{opposite}}{\text{hypotenuse}}\) and \(\csc \theta = \frac{1}{\sin \theta}\).
Given \(\sin \theta = \frac{1}{2}\), use the reciprocal identity to find \(\csc \theta\): \(\csc \theta = \frac{1}{\sin \theta} = \frac{1}{\frac{1}{2}}\).
Simplify the expression for \(\csc \theta\) to check if it equals 2, which is the value given in the problem.
Compare the calculated value of \(\csc \theta\) with the given value to determine if the statement is possible or impossible.
Conclude that if the values match, the statement is possible; if not, it is impossible.
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1mKey Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Definition of Sine and Cosecant Functions
Sine (sin θ) is the ratio of the length of the opposite side to the hypotenuse in a right triangle. Cosecant (csc θ) is the reciprocal of sine, defined as 1/sin θ. Understanding this reciprocal relationship is essential to verify if given values for sin θ and csc θ are consistent.
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Graphs of Secant and Cosecant Functions
Reciprocal Identities in Trigonometry
Reciprocal identities state that csc θ = 1/sin θ. This means if sin θ = 1/2, then csc θ must be 2. Recognizing these identities helps determine whether the given pair of values can coexist or if they contradict each other.
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Range and Possible Values of Trigonometric Functions
The sine function ranges between -1 and 1, so sin θ = 1/2 is possible. Since csc θ is the reciprocal, its values are outside the interval (-1, 1), so csc θ = 2 is also possible. Understanding these ranges helps assess the feasibility of the given values.
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Related Practice
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