Domanda del libro di testo
In the following exercises, (a) find the center-radius form of the equation of each circle described, and (b) graph it. See Examples 5 and 6. center (√2, √2), radius √2
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Ch. R - Algebra Review
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 1, Problema 59
Evaluate each expression. See Example 5. -|-2|
Guida verificata passo dopo passo1
Recognize that the expression involves the absolute value function, which returns the non-negative value of a number. The absolute value of a number \(x\) is denoted as \(|x|\) and is defined as \(|x| = x\) if \(x \geq 0\), and \(|x| = -x\) if \(x < 0\).
Start by evaluating the inner absolute value: calculate \(|-2|\). Since \(-2\) is negative, its absolute value is \(-(-2)\).
Simplify the inner absolute value: \(|-2| = 2\).
Now, evaluate the outer absolute value: \(|2|\). Since \(2\) is already positive, the absolute value remains \(2\).
Conclude that the value of the expression \(-|-2|\) is the negative of the inner absolute value, so it equals \(-2\).
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Absolute Value
The absolute value of a number is its distance from zero on the number line, always expressed as a non-negative value. For example, |−2| equals 2 because −2 is two units away from zero.
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Evaluate Composite Functions - Values Not on Unit Circle
Evaluating Expressions with Absolute Values
When evaluating expressions involving absolute values, first compute the absolute value part, then apply any remaining operations. For instance, in -|−2|, find |−2| = 2, then apply the negative sign to get -2.
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7:28Evaluate Composite Functions - Values Not on Unit Circle
Order of Operations
The order of operations dictates the sequence in which parts of an expression are evaluated. Absolute value is treated like parentheses and should be evaluated before applying multiplication, division, addition, or subtraction.
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04:12Algebraic Operations on Vectors
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Domanda del libro di testo
In the following exercises, (a) find the center-radius form of the equation of each circle described, and (b) graph it. See Examples 5 and 6.
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