Skip to main content
Ch. 3 - Trigonometric Identities and Equations
Blitzer - Trigonometry 3rd Edition
Blitzer3rd EditionTrigonometryISBN: 9780137316601Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoBlitzer 3rd EditionCh. 3 - Trigonometric Identities and EquationsProblema 15
Capitolo 3, Problema 15

In Exercises 15–22, write each expression as the sine, cosine, or tangent of a double angle. Then find the exact value of the expression. 2 sin 15° cos 15°

Guida verificata passo dopo passo
1
Recognize that the expression \(2 \sin 15^\circ \cos 15^\circ\) matches the double-angle identity for sine, which is \(2 \sin A \cos A = \sin 2A\).
Rewrite the expression using the identity: \(2 \sin 15^\circ \cos 15^\circ = \sin (2 \times 15^\circ)\).
Simplify the angle inside the sine function: \(\sin (30^\circ)\).
Recall the exact value of \(\sin 30^\circ\), which is a commonly known special angle in trigonometry.
Conclude that the exact value of the original expression is the exact value of \(\sin 30^\circ\).

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:
4m

Concetti chiave

Ecco i concetti essenziali che devi comprendere per rispondere correttamente alla domanda.

Double-Angle Identities

Double-angle identities express trigonometric functions of twice an angle in terms of functions of the original angle. For sine, the identity is sin(2θ) = 2 sin θ cos θ, which allows rewriting products like 2 sin 15° cos 15° as sin 30°.
Video consigliato:
Percorso guidato
05:06
Double Angle Identities

Evaluating Exact Trigonometric Values

Exact values of trigonometric functions at special angles (like 30°, 45°, 60°) are well-known and can be used to find precise results without a calculator. For example, sin 30° equals 1/2, which helps in determining the exact value of the expression.
Video consigliato:
Percorso guidato
5:10
Evaluate Composite Functions - Values on Unit Circle

Trigonometric Function Notation and Simplification

Understanding how to rewrite expressions using trigonometric notation and simplify them is essential. Recognizing patterns such as products of sine and cosine that match double-angle formulas enables efficient simplification and evaluation.
Video consigliato:
Percorso guidato
06:01
i & j Notation
Pratica correlata
Domanda del libro di testo

Use the given information to find the exact value of each of the following: sin 2θ

sin θ = ﹣2/3, θ lies in quadrant III.

821
views
Domanda del libro di testo

Find all solutions of each equation. cos x = ﹣1/2

539
views
Domanda del libro di testo

In Exercises 14–19, use a sum or difference formula to find the exact value of each expression. sin 195°

970
views
Domanda del libro di testo

Use the given information to find the exact value of each of the following: tan 2θ

sin θ = ﹣2/3, θ lies in quadrant III.

869
views
Domanda del libro di testo

Use the given information to find the exact value of each of the following: cos 2θ

sin θ = ﹣2/3, θ lies in quadrant III.

670
views
Domanda del libro di testo

Be sure that you've familiarized yourself with the second set of formulas presented in this section by working C5–C8 in the Concept and Vocabulary Check. In Exercises 9–22, express each sum or difference as a product. If possible, find this product's exact value. sin x + sin 2x

651
views