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 75
Find the exact values of s in the given interval that satisfy the given condition.
[0 , 2π) ; cos² s = 1/2
Guida verificata passo dopo passo1
Start with the given equation: \(\cos^{2} s = \frac{1}{2}\).
Take the square root of both sides to solve for \(\cos s\): \(\cos s = \pm \sqrt{\frac{1}{2}}\).
Simplify the square root: \(\cos s = \pm \frac{\sqrt{2}}{2}\).
Recall the unit circle values where \(\cos s = \pm \frac{\sqrt{2}}{2}\), which correspond to angles \(s = \frac{\pi}{4}, \frac{3\pi}{4}, \frac{5\pi}{4}, \frac{7\pi}{4}\) within the interval \([0, 2\pi)\).
List these values as the exact solutions for \(s\) in the given interval.
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Trigonometric Functions and Their Squares
The cosine function, cos(s), measures the horizontal coordinate of a point on the unit circle at angle s. Squaring the cosine, cos²(s), means taking the square of this value, which is always non-negative and ranges from 0 to 1. Understanding how cos²(s) relates to cos(s) is essential for solving equations involving squared trigonometric functions.
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Percorso guidato
6:04
Introduction to Trigonometric Functions
Unit Circle and Angle Intervals
The unit circle represents all angles s from 0 to 2π radians, corresponding to one full rotation. Knowing how cosine values correspond to points on the unit circle helps identify all angles s within the interval [0, 2π) that satisfy the equation. This includes recognizing symmetry and periodicity of cosine.
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Percorso guidato
06:11Introduction to the Unit Circle
Solving Trigonometric Equations
To solve equations like cos²(s) = 1/2, one must first find cos(s) = ±√(1/2) = ±√2/2. Then, determine all angles s in the given interval where cosine equals these values. This involves using inverse cosine functions and considering all solutions within the specified domain.
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4:34How to Solve Linear Trigonometric Equations
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