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Ch. 6 - Inverse Circular Functions and Trigonometric Equations
Lial - Trigonometry 12th Edition
Lial12th EditionTrigonometryISBN: 9780136552161, 9780135440780, 9780136881117, 9780135440827, 9780135924891Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoLial 12th EditionCh. 6 - Inverse Circular Functions and Trigonometric EquationsProblema 6.3.7
Capitolo 7, Problema 6.3.7

Solve for exact solutions over the interval [0°, 360°).
sin θ/2 = 0

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Start with the given equation: \(\frac{\sin \theta}{2} = 0\). This means that \(\sin \theta\) divided by 2 equals zero.
Multiply both sides of the equation by 2 to isolate \(\sin \theta\): \(\sin \theta = 0\).
Recall that \(\sin \theta = 0\) at specific angles within the interval \([0^\circ, 360^\circ)\), specifically where the sine function crosses the x-axis.
Identify the angles where \(\sin \theta = 0\) in the given interval. These are the angles where the terminal side of \(\theta\) lies along the x-axis.
Write down the exact solutions for \(\theta\) in degrees within \([0^\circ, 360^\circ)\) where \(\sin \theta = 0\).

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Solving Basic Trigonometric Equations

To solve equations like sin(θ/2) = 0, identify the angles where the sine function equals zero. Since sine is zero at integer multiples of 180°, set the argument θ/2 equal to these values and solve for θ within the given interval.
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How to Solve Linear Trigonometric Equations

Understanding the Domain and Interval Restrictions

The problem restricts θ to the interval [0°, 360°), so solutions must be found only within this range. After solving for θ, verify that each solution lies within the specified interval to ensure validity.
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Finding the Domain of an Equation

Angle Multiplication and Division in Trigonometric Functions

When the variable is inside the function with a coefficient (like θ/2), adjust the equation accordingly by multiplying or dividing to isolate θ. This step is crucial to correctly find all possible solutions within the interval.
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Introduction to Trigonometric Functions
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