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Concept Check Suppose that 90° < θ < 180° . Find the sign of each function value. cos ( ―θ)
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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 95
Find the angle of least positive measure (not equal to the given measure) that is coterminal with each angle. -5280°
Guida verificata passo dopo passo1
Understand that coterminal angles differ by full rotations of 360°. To find an angle coterminal with the given angle, you add or subtract multiples of 360°.
Given the angle is \(-5280^\circ\), start by adding 360° repeatedly until you get an angle between 0° and 360°, which will be the least positive coterminal angle.
Express this mathematically as: \(\theta = -5280^\circ + 360^\circ \times k\), where \(k\) is an integer chosen so that \(0^\circ < \theta < 360^\circ\).
Calculate the value of \(k\) by dividing 5280 by 360 and finding the smallest integer \(k\) such that \(\theta\) is positive and less than 360°.
Once you find the correct \(k\), substitute back into the equation to find the least positive coterminal angle different from the original \(-5280^\circ\).
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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 angles that have the same trigonometric values.
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Percorso guidato
04:46
Coterminal Angles
Angle Reduction to Least Positive Measure
Reducing an angle to its least positive coterminal measure involves finding the smallest positive angle between 0° and 360° that is coterminal with the given angle. This is done by repeatedly adding or subtracting 360° until the angle lies within this range.
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Percorso guidato
05:50Drawing Angles in Standard Position
Modulo Operation in Angle Measurement
Using modulo 360° arithmetic simplifies finding coterminal angles by effectively 'wrapping' the angle within a 0° to 360° cycle. The remainder after dividing the angle by 360° gives the equivalent angle within one full rotation, aiding in quick calculation of coterminal angles.
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Percorso guidato
5:31Reference Angles on the Unit Circle
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