Textbook Question
Give all six trigonometric function values for each angle θ. Rationalize denominators when applicable. See Examples 5–7.
csc θ = ―3 , and cos θ > 0
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Ch. 1 - Trigonometric Functions
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 2, Problem 79
Find the angle of least positive measure (not equal to the given measure) that is coterminal with each angle. See Example 5. 26° 30'
Verified step by step guidance1
Understand that coterminal angles differ by full rotations of 360°. To find angles coterminal with a given angle, you add or subtract multiples of 360°.
Convert the given angle 26° 30' into decimal degrees or work directly with degrees and minutes. Here, 30 minutes is half a degree, so 26° 30' = 26.5°.
To find the least positive coterminal angle different from 26° 30', subtract 360° from 26.5° to get a negative angle, which is not positive, so discard this.
Add 360° to 26.5° to find the next positive coterminal angle: 26.5° + 360° = 386.5°.
Convert the decimal coterminal angle back to degrees and minutes if needed. For example, 0.5° equals 30 minutes, so 386.5° = 386° 30'. This is the least positive coterminal angle different from the original.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
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 position on the unit circle.
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Coterminal Angles
Angle Measurement in Degrees and Minutes
Angles can be expressed in degrees (°) and minutes (') where 1 degree equals 60 minutes. Understanding how to convert and manipulate these units is essential for precise calculations, especially when adding or subtracting angles given in degrees and minutes.
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5:31Reference Angles on the Unit Circle
Least Positive Angle
The least positive angle coterminal with a given angle is the smallest positive angle greater than 0° that shares the same terminal side. It is found by adjusting the angle within the range of 0° to 360°, excluding the original angle, to find the minimal positive equivalent.
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05:50Drawing Angles in Standard Position
Related Practice
Textbook Question
Give all six trigonometric function values for each angle θ. Rationalize denominators when applicable. See Examples 5–7.
sin θ = √2/6 , and cos θ < 0
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Textbook Question
Find the indicated function value. If it is undefined, say so. See Example 4. cos 1800°
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Textbook Question
Convert each angle measure to degrees, minutes, and seconds. If applicable, round to the nearest second. 122.6853°
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Textbook Question
Give all six trigonometric function values for each angle θ. Rationalize denominators when applicable. See Examples 5–7.
sin θ = √5/7 , and θ is in quadrant I.
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Textbook Question
Find the indicated function value. If it is undefined, say so. See Example 4. sec 1800°
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