Skip to main content
Ch. 1 - Trigonometric Functions
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. 1 - Trigonometric FunctionsProblema 84
Capitolo 2, Problema 84

Give all six trigonometric function values for each angle θ. Rationalize denominators when applicable. See Examples 5–7.
cos θ = 1

Guida verificata passo dopo passo
1
Identify the given trigonometric function and its value: here, \( \cos \theta = 1 \).
Recall the definition of cosine in terms of the unit circle: \( \cos \theta = \frac{x}{r} \), where \( x \) is the horizontal coordinate and \( r = 1 \) on the unit circle.
Determine the angle(s) \( \theta \) where \( \cos \theta = 1 \). On the unit circle, this occurs at \( \theta = 0 \) (or multiples of \( 2\pi \)).
Use the Pythagorean identity to find \( \sin \theta \): \( \sin^2 \theta + \cos^2 \theta = 1 \). Substitute \( \cos \theta = 1 \) to find \( \sin \theta \).
Calculate the remaining trigonometric functions using their definitions: \( \tan \theta = \frac{\sin \theta}{\cos \theta} \), \( \csc \theta = \frac{1}{\sin \theta} \), \( \sec \theta = \frac{1}{\cos \theta} \), and \( \cot \theta = \frac{1}{\tan \theta} \). Rationalize denominators if needed.

Risposta video verificata per un problema simile:

Questa soluzione video è stata consigliata dai nostri tutor come utile per risolvere questo problema.

Concetti chiave

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

Definition of the Six Trigonometric Functions

The six trigonometric functions—sine, cosine, tangent, cosecant, secant, and cotangent—are ratios of sides in a right triangle or coordinates on the unit circle. Given one function value, the others can be found using their interrelationships and identities.
Video consigliato:
Percorso guidato
6:04
Introduction to Trigonometric Functions

Unit Circle and Angle Interpretation

The unit circle represents angles as points (x, y) where x = cos θ and y = sin θ. Knowing cos θ = 1 corresponds to the point (1, 0), which helps determine all other function values for that angle.
Video consigliato:
Percorso guidato
06:11
Introduction to the Unit Circle

Rationalizing Denominators

Rationalizing denominators involves eliminating radicals from the denominator of a fraction by multiplying numerator and denominator by a suitable expression. This is often required for final answers to be in simplified, standard form.
Video consigliato:
Percorso guidato
2:58
Rationalizing Denominators
Pratica correlata
Domanda del libro di testo

Give all six trigonometric function values for each angle θ. Rationalize denominators when applicable. See Examples 5–7.

csc θ = ―3 , and cos θ > 0

685
views
Domanda del libro di testo

Give all six trigonometric function values for each angle θ. Rationalize denominators when applicable. See Examples 5–7.

sin θ = √2/6 , and cos θ < 0

815
views
Domanda del libro di testo

Find the angle of least positive measure (not equal to the given measure) that is coterminal with each angle. ―203° 20'

659
views
Domanda del libro di testo

Use trigonometric function values of quadrantal angles to evaluate each expression. 3 sec 180° ― 5 tan 360°

597
views
Domanda del libro di testo

Find the angle of least positive measure (not equal to the given measure) that is coterminal with each angle. See Example 5. 541°

676
views
Domanda del libro di testo

Find the indicated function value. If it is undefined, say so. See Example 4. sec 1800°

662
views