Domanda del libro di testo
Find the unknown side lengths in each pair of similar triangles.
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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 20
Use the appropriate reciprocal identity to find each function value. Rationalize denominators when applicable. See Example 1.
sin θ , given that csc θ = √24/3
Guida verificata passo dopo passo1
Recall the reciprocal identity relating sine and cosecant: \(\sin \theta = \frac{1}{\csc \theta}\).
Substitute the given value of \(\csc \theta = \frac{\sqrt{24}}{3}\) into the identity: \(\sin \theta = \frac{1}{\frac{\sqrt{24}}{3}}\).
Simplify the complex fraction by multiplying numerator and denominator appropriately: \(\sin \theta = \frac{3}{\sqrt{24}}\).
Rationalize the denominator by multiplying numerator and denominator by \(\sqrt{24}\): \(\sin \theta = \frac{3 \times \sqrt{24}}{\sqrt{24} \times \sqrt{24}}\).
Simplify the denominator using the property \(\sqrt{a} \times \sqrt{a} = a\) and reduce the fraction if possible to express \(\sin \theta\) in simplest form.
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Reciprocal Identities
Reciprocal identities relate trigonometric functions to their reciprocals, such as sin θ = 1/csc θ. These identities allow you to find one function value when its reciprocal is known, simplifying calculations and problem-solving.
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Percorso guidato
6:25
Pythagorean Identities
Rationalizing the Denominator
Rationalizing the denominator involves eliminating any radicals from the denominator of a fraction by multiplying numerator and denominator by a suitable expression. This process makes the expression simpler and more standard in form.
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Percorso guidato
2:58Rationalizing Denominators
Simplifying Radicals
Simplifying radicals means expressing square roots in their simplest form by factoring out perfect squares. This helps in reducing expressions like √24 to 2√6, making calculations and rationalization easier.
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Percorso guidato
6:36Simplifying Trig Expressions
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