Skip to main content
Ch. 1 - Angles and the Trigonometric Functions
Blitzer - Trigonometry 3rd Edition
Blitzer3rd EditionTrigonometryISBN: 9780137316601Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoBlitzer 3rd EditionCh. 1 - Angles and the Trigonometric FunctionsProblema 1.19a
Capitolo 1, Problema 1.19a

Use the unit circle shown to find the value of the trigonometric function.
cos 𝜋/6

Guida verificata passo dopo passo
1
Identify the angle \( \frac{\pi}{6} \) on the unit circle. This angle corresponds to 30 degrees.
Recall that the unit circle is a circle with a radius of 1 centered at the origin of the coordinate plane.
On the unit circle, the coordinates of a point corresponding to an angle \( \theta \) are \((\cos \theta, \sin \theta)\).
For \( \theta = \frac{\pi}{6} \), find the x-coordinate of the point on the unit circle, which represents \( \cos \frac{\pi}{6} \).
Use the known values from the unit circle: \( \cos \frac{\pi}{6} = \frac{\sqrt{3}}{2} \).

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:
1m

Concetti chiave

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

Unit Circle

The unit circle is a circle with a radius of one centered at the origin of a coordinate plane. It is a fundamental tool in trigonometry, as it allows for the definition of trigonometric functions based on the coordinates of points on the circle. The x-coordinate of a point on the unit circle corresponds to the cosine of the angle, while the y-coordinate corresponds to the sine.
Video consigliato:
Percorso guidato
06:11
Introduction to the Unit Circle

Cosine Function

The cosine function, denoted as cos(θ), represents the x-coordinate of a point on the unit circle corresponding to an angle θ measured from the positive x-axis. For angles measured in radians, such as π/6, the cosine function provides a specific value that can be derived from the coordinates of the corresponding point on the unit circle.
Video consigliato:
Percorso guidato
5:53
Graph of Sine and Cosine Function

Reference Angles

Reference angles are the acute angles formed by the terminal side of an angle and the x-axis. They are crucial for determining the values of trigonometric functions in different quadrants. For example, the angle π/6 has a reference angle of π/6 itself, which helps in finding its cosine value directly from the unit circle.
Video consigliato:
Percorso guidato
5:31
Reference Angles on the Unit Circle
Pratica correlata
Domanda del libro di testo

Use the unit circle shown to find the value of the trigonometric function.

sin (2𝜋/3)

692
views
Domanda del libro di testo

Use the unit circle shown to find the value of the trigonometric function.

tan 11𝜋/6

972
views
Domanda del libro di testo

Find the length of the arc on a circle of radius 20 feet intercepted by a 75° central angle. Express arc length in terms of 𝜋. Then round your answer to two decimal places.

602
views
Domanda del libro di testo

In Exercises 1–4, a point P(x, y) is shown on the unit circle corresponding to a real number t. Find the values of the trigonometric functions at t.

813
views
Domanda del libro di testo

The unit circle has been divided into eight equal arcs, corresponding to t-values of


0, 𝜋/4, 𝜋/2, 3𝜋/4, 𝜋, 5𝜋/4, 3𝜋/2, 7𝜋/4, and 2𝜋.


a. Use the (x,y) coordinates in the figure to find the value of the trigonometric function.

b. Use periodic properties and your answer from part (a) to find the value of the same trigonometric function at the indicated real number.

<IMAGE>


sin 3𝜋/4

604
views
Domanda del libro di testo

In Exercises 2–4, convert each angle in degrees to radians. Express your answer as a multiple of 𝜋. 15°

547
views