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CONCEPT PREVIEW Determine whether each statement is possible or impossible. sin θ = 1/2 , csc θ = 2
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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 4
Find the angle of least positive measure that is coterminal with each angle. 792°
Guida verificata passo dopo passo1
Understand that angles are coterminal if they differ by full rotations of 360°. To find an angle coterminal with 792°, we need to subtract multiples of 360° until the result is between 0° and 360°.
Set up the expression to find the coterminal angle: \(\theta = 792^\circ - 360^\circ \times k\), where \(k\) is an integer chosen so that \(0^\circ \leq \theta < 360^\circ\).
Determine the appropriate value of \(k\) by dividing 792 by 360: \(\frac{792}{360} = 2.2\). Since \(k\) must be an integer, try \(k=2\).
Calculate the coterminal angle using \(k=2\): \(\theta = 792^\circ - 360^\circ \times 2\).
Verify that the resulting angle \(\theta\) is between 0° and 360°, which will be the least positive angle coterminal with 792°.
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Coterminal Angles
Coterminal angles are angles that share the same initial and terminal sides but differ by full rotations of 360°. To find coterminal angles, you add or subtract multiples of 360° from the given angle. This concept helps identify equivalent angles within a standard range.
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Percorso guidato
04:46
Coterminal Angles
Angle Reduction to Least Positive Measure
The least positive measure of an angle is the smallest positive angle coterminal with the given angle, typically between 0° and 360°. To find it, repeatedly subtract 360° from the angle until the result lies within this range, ensuring the angle is positive and minimal.
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Percorso guidato
05:50Drawing Angles in Standard Position
Modular Arithmetic in Angle Measurement
Modular arithmetic simplifies angle calculations by treating angles modulo 360°. This means angles differing by multiples of 360° are equivalent, allowing easy computation of coterminal angles using the remainder after division by 360°. It streamlines finding standard angle measures.
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5:31Reference Angles on the Unit Circle
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