Skip to main content
Ch. 2 - Acute Angles and Right Triangles
Lial - Trigonometry 12th Edition
Lial12th EditionTrigonometryISBN: 9780136552161, 9780135440780, 9780136881117, 9780135440827, 9780135924891Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoLial 12th EditionCh. 2 - Acute Angles and Right TrianglesProblema 36
Capitolo 3, Problema 36

Find exact values of the six trigonometric functions of each angle. Rationalize denominators when applicable. See Examples 2, 3, and 5. -2205°

Guida verificata passo dopo passo
1
Step 1: Understand that the angle given is -2205°, which is a negative angle. To find the trigonometric functions, first convert this angle to a positive coterminal angle between 0° and 360° by adding multiples of 360° until the angle lies within this range. Use the formula: \(\theta_{coterminal} = \theta + 360k\), where \(k\) is an integer chosen to make \(\theta_{coterminal}\) between 0° and 360°.
Step 2: Calculate the coterminal angle by adding 360° repeatedly to -2205° until the result is between 0° and 360°. This will give you an equivalent angle that has the same trigonometric values as -2205°.
Step 3: Once you have the coterminal angle, determine the reference angle. The reference angle is the acute angle formed between the terminal side of the coterminal angle and the x-axis. This helps in finding the exact values of the trigonometric functions.
Step 4: Identify the quadrant in which the coterminal angle lies. The signs of the six trigonometric functions (sine, cosine, tangent, cosecant, secant, cotangent) depend on the quadrant. Recall the ASTC rule (All Students Take Calculus) to determine the signs.
Step 5: Use known exact values of trigonometric functions for standard angles (like 30°, 45°, 60°, etc.) and apply the appropriate sign based on the quadrant to find the exact values of all six trigonometric functions. Rationalize denominators if necessary.

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:
9m

Concetti chiave

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

Angle Reduction Using Coterminal Angles

Angles larger than 360° or negative angles can be simplified by adding or subtracting multiples of 360° to find a coterminal angle between 0° and 360°. This helps in evaluating trigonometric functions by referencing standard angle values.
Video consigliato:
Percorso guidato
04:46
Coterminal Angles

Definition of the Six Trigonometric Functions

The six trigonometric functions—sine, cosine, tangent, cosecant, secant, and cotangent—are ratios derived from a right triangle or the unit circle. Understanding their definitions and relationships is essential for calculating exact values.
Video consigliato:
Percorso guidato
6:04
Introduction to Trigonometric Functions

Rationalizing Denominators

Rationalizing denominators involves eliminating radicals from the denominator of a fraction by multiplying numerator and denominator by a suitable expression. This is important for expressing trigonometric values in a simplified, exact form.
Video consigliato:
Percorso guidato
2:58
Rationalizing Denominators
Pratica correlata
Domanda del libro di testo

Find one solution for each equation. Assume all angles involved are acute angles. See Example 3. cos(2θ + 50°) = sin(2θ - 20°)

585
views
Domanda del libro di testo

Solve each right triangle. In each case, C = 90°. If angle information is given in degrees and minutes, give answers in the same way. If angle information is given in decimal degrees, do likewise in answers. When two sides are given, give angles in degrees and minutes. See Examples 1 and 2. a = 958 m, b = 489 m

603
views
Domanda del libro di testo

Find the exact value of each expression. See Example 3. sin 1305°

635
views
Domanda del libro di testo

Find exact values of the six trigonometric functions of each angle. Rationalize denominators when applicable. See Examples 2, 3, and 5. -1860°

675
views
Domanda del libro di testo

Solve each right triangle. In each case, C = 90°. If angle information is given in degrees and minutes, give answers in the same way. If angle information is given in decimal degrees, do likewise in answers. When two sides are given, give angles in degrees and minutes. See Examples 1 and 2. A = 53°24', c = 387.1 ft

581
views
Domanda del libro di testo

Find one solution for each equation. Assume all angles involved are acute angles. See Example 3. cot(5θ + 2°) = tan(2θ + 4°)

633
views