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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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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 2, Problema 5
CONCEPT PREVIEW Determine whether each statement is possible or impossible. sin θ = 1/2 , csc θ = 2
Guida verificata passo dopo passo1
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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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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Percorso guidato
6:22
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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Percorso guidato
5:32Fundamental Trigonometric Identities
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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Percorso guidato
4:22Domain and Range of Function Transformations
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