Domanda del libro di testo
Find the angle of least positive measure (not equal to the given measure) that is coterminal with each angle. ―541°
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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 91
Concept Check Suppose that 90° < θ < 180° . Find the sign of each function value. tan θ/2
Guida verificata passo dopo passo1
Identify the quadrant where \( \theta \) lies. Since \( 90^\circ < \theta < 180^\circ \), \( \theta \) is in the second quadrant.
Determine the range of \( \frac{\theta}{2} \). Since \( \theta \) is between \( 90^\circ \) and \( 180^\circ \), dividing by 2 gives \( 45^\circ < \frac{\theta}{2} < 90^\circ \). This means \( \frac{\theta}{2} \) lies in the first quadrant.
Recall the signs of tangent in each quadrant. Tangent is positive in the first and third quadrants, and negative in the second and fourth quadrants.
Since \( \frac{\theta}{2} \) is in the first quadrant, \( \tan \frac{\theta}{2} \) is positive.
Therefore, the sign of \( \tan \frac{\theta}{2} \) is positive for \( 90^\circ < \theta < 180^\circ \).
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Angle Quadrants and Their Ranges
The coordinate plane is divided into four quadrants, each with specific angle ranges and sign conventions for trigonometric functions. For 90° < θ < 180°, θ lies in the second quadrant, where sine is positive and cosine is negative. Understanding the quadrant helps determine the sign of trigonometric values.
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Percorso guidato
6:36
Quadratic Formula
Half-Angle Relationships
The half-angle θ/2 is half the measure of the original angle θ. When θ is between 90° and 180°, θ/2 lies between 45° and 90°, placing it in the first quadrant. This affects the sign of trigonometric functions of θ/2, as signs depend on the quadrant of the angle.
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Percorso guidato
04:46Coterminal Angles
Sign of the Tangent Function
The tangent function is positive in the first and third quadrants and negative in the second and fourth quadrants. Since θ/2 lies between 45° and 90° (first quadrant), tan(θ/2) is positive. Recognizing the quadrant of θ/2 is essential to determine the sign of tan(θ/2).
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Percorso guidato
5:43Introduction to Tangent Graph
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