Domanda del libro di testo
Fill in the blank(s) to correctly complete each sentence.
An equilateral triangle has _________________ equal sides.
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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 2
CONCEPT PREVIEW Fill in the blank(s) to correctly complete each sentence. Given tan θ = 1/cot θ , two equivalent forms of this identity are cot θ = 1/______ and tan θ . ______ = 1 .
Guida verificata passo dopo passo1
Recall the definitions of the tangent and cotangent functions: \(\tan \theta = \frac{\sin \theta}{\cos \theta}\) and \(\cot \theta = \frac{\cos \theta}{\sin \theta}\).
Given the identity \(\tan \theta = \frac{1}{\cot \theta}\), rewrite \(\cot \theta\) in terms of \(\tan \theta\) by taking the reciprocal of both sides, which gives \(\cot \theta = \frac{1}{\tan \theta}\).
The first blank corresponds to the expression for \(\cot \theta\) in terms of \(\tan \theta\), so fill it with \(\tan \theta\).
For the second blank, consider the product \(\tan \theta \cdot \cot \theta\). Using the reciprocal relationship, this product equals 1, so fill the blank with \(\cot \theta\).
Summarize the equivalent forms: \(\cot \theta = \frac{1}{\tan \theta}\) and \(\tan \theta \cdot \cot \theta = 1\).
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Reciprocal Identities
Reciprocal identities in trigonometry express the relationship between pairs of functions such as tangent and cotangent. Specifically, tan θ is the reciprocal of cot θ, meaning tan θ = 1/cot θ and cot θ = 1/tan θ. Understanding these helps in rewriting and simplifying trigonometric expressions.
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Percorso guidato
6:25
Pythagorean Identities
Definition of Tangent and Cotangent
Tangent of an angle θ is defined as the ratio of the sine to the cosine of θ (tan θ = sin θ / cos θ), while cotangent is the inverse ratio (cot θ = cos θ / sin θ). Recognizing these definitions clarifies why tan θ and cot θ are reciprocals.
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Percorso guidato
5:37Introduction to Cotangent Graph
Multiplicative Inverse Property
The multiplicative inverse property states that a number multiplied by its reciprocal equals one. Applying this to trigonometric functions, tan θ multiplied by cot θ equals 1, reinforcing the identity tan θ * cot θ = 1.
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Percorso guidato
4:49Inverse Cosine
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