Domanda del libro di testo
In Exercises 61–86, use reference angles to find the exact value of each expression. Do not use a calculator. sin(2𝜋/3)
655
views
Ch. 1 - Angles and the Trigonometric Functions
Blitzer3rd EditionTrigonometryISBN: 9780137316601
Non è quello che usi tu?Cambia libro di testoScegli un libro di testo diverso
TOC.tableOfContents
Tutti i libri di testo
Blitzer 3rd EditionCh. 1 - Angles and the Trigonometric FunctionsProblema 1.2.68
Blitzer 3rd EditionCh. 1 - Angles and the Trigonometric FunctionsProblema 1.2.68Capitolo 1, Problema 1.2.68
In Exercises 63–68, find the exact value of each expression. Do not use a calculator. cos 12° sin 78° + cos 78° sin 12°
Guida verificata passo dopo passo1
Recognize that the expression \( \cos 12^\circ \sin 78^\circ + \cos 78^\circ \sin 12^\circ \) matches the form of the sine addition formula, which is \( \sin(A + B) = \sin A \cos B + \cos A \sin B \).
Identify the angles in the expression to match the formula: let \( A = 78^\circ \) and \( B = 12^\circ \), so the expression becomes \( \cos 12^\circ \sin 78^\circ + \cos 78^\circ \sin 12^\circ = \sin(78^\circ + 12^\circ) \).
Add the angles inside the sine function: \( 78^\circ + 12^\circ = 90^\circ \), so the expression simplifies to \( \sin 90^\circ \).
Recall the exact value of \( \sin 90^\circ \), which is a fundamental trigonometric value.
Conclude that the original expression is equal to \( \sin 90^\circ \), and thus find the exact value without using a calculator.
Risposta video verificata per un problema simile:
Questa soluzione video è stata consigliata dai nostri tutor come utile per risolvere questo problema.
Durata del video:
3mConcetti chiave
Ecco i concetti essenziali che devi comprendere per rispondere correttamente alla domanda.
Sum of Angles Identity for Sine
The sum of angles identity states that sin(A + B) = sin A cos B + cos A sin B. This formula allows the expression cos 12° sin 78° + cos 78° sin 12° to be recognized as sin(12° + 78°), simplifying the calculation without a calculator.
Video consigliato:
Percorso guidato
06:14
Sum and Difference of Sine & Cosine
Exact Values of Trigonometric Functions
Exact values refer to the precise trigonometric values for special angles, often expressed in fractions or radicals. Knowing these values or how to simplify expressions to standard angles like 90° helps find exact results without decimal approximations.
Video consigliato:
Percorso guidato
6:04Introduction to Trigonometric Functions
Angle Complementarity in Trigonometry
Complementary angles sum to 90°, and their sine and cosine values are related: sin θ = cos(90° - θ). Recognizing complementary angles can simplify expressions and help verify results, especially when dealing with angles like 12° and 78°.
Video consigliato:
Percorso guidato
3:35Intro to Complementary & Supplementary Angles
Pratica correlata
Domanda del libro di testo
In Exercises 1–8, a point on the terminal side of angle θ is given. Find the exact value of each of the six trigonometric functions of θ. (-4, 3)
542
views
Domanda del libro di testo
In Exercises 41–56, use the circle shown in the rectangular coordinate system to draw each angle in standard position. State the quadrant in which the angle lies. When an angle's measure is given in radians, work the exercise without converting to degrees.
120°
635
views
Domanda del libro di testo
In Exercises 57–70, find a positive angle less than or that is coterminal with the given angle. 395°
679
views
Domanda del libro di testo
In Exercises 71–74, find the length of the arc on a circle of radius r intercepted by a central angle θ. Express arc length in terms of 𝜋. Then round your answer to two decimal places. Radius, r: 12 inches Central Angle, θ: θ = 45°
702
views
Domanda del libro di testo
In Exercises 61–86, use reference angles to find the exact value of each expression. Do not use a calculator. cot(7𝜋/4)
657
views