Ch. 2 - Acute Angles and Right Triangles

Lial12th EditionTrigonometryISBN: 9780136552161, 9780135440780, 9780136881117, 9780135440827, 9780135924891Non è quello che usi tu?Cambia libro di testo

Lial 12th Edition

Ch. 2 - Acute Angles and Right Triangles

Problema 6

Capitolo 3, Problema 6

Find one solution for each equation. Assume all angles involved are acute angles. cos(3θ + 11°) = sin( 7θ + 40°) 5 10

Guida verificata passo dopo passo

Recall the co-function identity in trigonometry: \(\cos A = \sin B\) implies that either \(A = B\) or \(A = 90^\circ - B\) (considering acute angles).

Set up the first equation by equating the angles directly: \(3\theta + 11^\circ = 7\theta + 40^\circ\).

Solve the equation from step 2 for \(\theta\) by isolating \(\theta\) on one side.

Set up the second equation using the complementary angle relationship: \(3\theta + 11^\circ = 90^\circ - (7\theta + 40^\circ)\).

Solve the equation from step 4 for \(\theta\) by simplifying and isolating \(\theta\).

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:

Concetti chiave

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

Trigonometric Identities

Trigonometric identities are equations that involve trigonometric functions and are true for all values of the variables. Key identities include the Pythagorean identity, reciprocal identities, and co-function identities. For instance, the identity sin(x) = cos(90° - x) can be useful in transforming equations to find solutions involving sine and cosine functions.

Video consigliato:

Percorso guidato

5:32

Fundamental Trigonometric Identities

Angle Addition Formulas

Angle addition formulas allow us to express the sine and cosine of the sum of two angles in terms of the sines and cosines of the individual angles. For example, cos(A + B) = cos(A)cos(B) - sin(A)sin(B) and sin(A + B) = sin(A)cos(B) + cos(A)sin(B). These formulas are essential for simplifying expressions like cos(3θ + 11°) and sin(7θ + 40°) in the given equation.

Video consigliato:

Percorso guidato

6:36

Quadratic Formula

Acute Angles in Trigonometry

Acute angles are angles that measure less than 90 degrees. In trigonometry, the values of sine and cosine for acute angles are always positive, which is important when solving equations involving these functions. Understanding the behavior of trigonometric functions in the context of acute angles helps in determining valid solutions for the given equation.

Video consigliato:

Percorso guidato

05:50

Drawing Angles in Standard Position

Pratica correlata

Domanda del libro di testo

Match each trigonometric function in Column I with its value in Column II. Choices may be used once, more than once, or not at all.

cot 30°

446

views

Domanda del libro di testo

Concept Check Match each angle in Column I with its reference angle in Column II. Choices may be used once, more than once, or not at all. See Example 1. I. II. 5. A. 45° 6. B. 60° 7. -135° C. 82° 8. D. 30° 9. E. 38° 10. F. 32°

666

views

Domanda del libro di testo

Concept Check Match each angle in Column I with its reference angle in Column II. Choices may be used once, more than once, or not at all. See Example 1. I. II. 5. A. 45° 6. 212° B. 60° 7. C. 82° 8. D. 30° 9. E. 38° 10. F. 32°

627

views

Domanda del libro di testo

CONCEPT PREVIEW Match each trigonometric function value or angle in Column I with its appropriate approximation in Column II.

Column I: 1.

sec 18°

Column II:

A. 88.09084757°

B. 63.25631605°

C. 1.909152433°

D. 17.45760312°

E. 0.2867453858