Domanda del libro di testo
Concept Check Suppose that ―90° < θ < 90° . Find the sign of each function value. sec 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 99
Give two positive and two negative angles that are coterminal with the given quadrantal angle. 0°
Guida verificata passo dopo passo1
Recall that coterminal angles differ by full rotations of 360°. This means if \( \theta \) is an angle, then angles coterminal with \( \theta \) can be found by adding or subtracting multiples of 360°: \( \theta + 360k \), where \( k \) is any integer.
Given the angle \( 0^\circ \), find two positive coterminal angles by adding 360° and 720° (which are \( 360 \times 1 \) and \( 360 \times 2 \)) to 0°.
Similarly, find two negative coterminal angles by subtracting 360° and 720° (which are \( 360 \times (-1) \) and \( 360 \times (-2) \)) from 0°.
Write down the positive coterminal angles as \( 0^\circ + 360^\circ = 360^\circ \) and \( 0^\circ + 720^\circ = 720^\circ \).
Write down the negative coterminal angles as \( 0^\circ - 360^\circ = -360^\circ \) and \( 0^\circ - 720^\circ = -720^\circ \).
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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°. Adding or subtracting multiples of 360° to an angle results in coterminal angles. For example, 0° and 360° are coterminal.
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Percorso guidato
04:46
Coterminal Angles
Quadrantal Angles
Quadrantal angles are angles whose terminal side lies along the x-axis or y-axis, typically 0°, 90°, 180°, 270°, or 360°. These angles are important because their trigonometric values are often simple or undefined, and they serve as reference points on the unit circle.
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Percorso guidato
6:36Quadratic Formula
Positive and Negative Angle Measures
Positive angles are measured counterclockwise from the initial side, while negative angles are measured clockwise. Understanding this helps in finding coterminal angles by adding positive or negative multiples of 360°, ensuring the angles remain coterminal but differ in sign.
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Percorso guidato
05:50Drawing Angles in Standard Position
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If n is an integer, n • 180° represents an integer multiple of 180°, (2n + 1) • 90° represents an odd integer multiple of 90° , and so on. Determine whether each expression is equal to 0, 1, or ―1, or is undefined. sin[n • 180°]
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Domanda del libro di testo
Concept Check Suppose that ―90° < θ < 90° . Find the sign of each function value.
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Give two positive and two negative angles that are coterminal with the given quadrantal angle. 270°
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Domanda del libro di testo
Give two positive and two negative angles that are coterminal with the given quadrantal angle. 90°
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Use trigonometric function values of quadrantal angles to evaluate each expression. [cos(―180°)]² + [sin(― 180°)]²
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