Domanda del libro di testo
Perform each calculation. See Example 3. 90° ― 51° 28'
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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 45b
Determine whether each statement is possible or impossible. b. tan θ = 1.4
Guida verificata passo dopo passo1
Recall that the tangent function, \(\tan \theta\), is defined as the ratio of the sine and cosine of an angle: \(\tan \theta = \frac{\sin \theta}{\cos \theta}\).
Understand that the range of the tangent function is all real numbers, meaning \(\tan \theta\) can take any real value from \(-\infty\) to \(+\infty\).
Since \(1.4\) is a real number, check if it lies within the range of possible values for \(\tan \theta\). Because the tangent function can be any real number, \(1.4\) is within this range.
Conclude that there exists some angle \(\theta\) such that \(\tan \theta = 1.4\), making the statement possible.
Optionally, to find such an angle, you could use the inverse tangent function: \(\theta = \tan^{-1}(1.4)\), which will give an angle in radians or degrees.
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Concetti chiave
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Definition and Range of the Tangent Function
The tangent of an angle θ in a right triangle is defined as the ratio of the opposite side to the adjacent side. Unlike sine and cosine, tangent values can range from negative to positive infinity, meaning any real number is a possible value for tan θ.
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Percorso guidato
4:22
Domain and Range of Function Transformations
Domain and Range of Tangent on the Unit Circle
On the unit circle, tan θ is defined as sin θ divided by cos θ. Since cosine can be zero, tan θ is undefined at odd multiples of 90°, but between these points, tan θ takes all real values, including 1.4, making such values possible.
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Percorso guidato
5:10Finding the Domain and Range of a Graph
Determining Possibility of a Tangent Value
To determine if tan θ = 1.4 is possible, consider that tangent can take any real number except where cosine is zero. Since 1.4 is a real number and not restricted by the function's domain, tan θ = 1.4 is possible for some angle θ.
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Percorso guidato
5:08Sine, Cosine, & Tangent of 30°, 45°, & 60°
Pratica correlata
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