Domanda del libro di testo
Find each exact function value. See Example 3.
sin 5π/6
689
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Ch. 3 - Radian Measure and The Unit Circle
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 4, Problema 77
Find the exact values of s in the given interval that satisfy the given condition.
[-2π , π) ; 3 tan² s = 1
Guida verificata passo dopo passo1
Start by writing down the given equation: \(3 \tan^{2} s = 1\).
Isolate \(\tan^{2} s\) by dividing both sides of the equation by 3: \(\tan^{2} s = \frac{1}{3}\).
Take the square root of both sides to solve for \(\tan s\): \(\tan s = \pm \frac{1}{\sqrt{3}}\).
Recall that \(\tan s = \pm \frac{1}{\sqrt{3}}\) corresponds to specific reference angles where tangent has these values. Identify these angles within one full period of tangent, which is \(\pi\).
Find all values of \(s\) in the interval \([-2\pi, \pi)\) by adding integer multiples of \(\pi\) to the reference angles, and then select those that lie within the given interval.
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Solving Trigonometric Equations
Solving trigonometric equations involves finding all angle values that satisfy the given equation within a specified interval. This often requires isolating the trigonometric function and using inverse functions or known identities to determine possible solutions.
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Percorso guidato
4:34
How to Solve Linear Trigonometric Equations
Properties of the Tangent Function
The tangent function, tan(s), is periodic with period π and is undefined at odd multiples of π/2. Understanding its behavior, including its range and periodicity, is essential for finding all solutions within a given interval.
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Percorso guidato
5:43Introduction to Tangent Graph
Interval Notation and Solution Sets
The interval [-2π, π) specifies the domain in which solutions must be found, including -2π but excluding π. Correctly interpreting this interval ensures that all valid solutions are identified and extraneous ones outside the range are excluded.
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Percorso guidato
06:01i & j Notation
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s = 2.5
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