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 32
Capitolo 1, Problema 32

Find a cofunction with the same value as the given expression.
sin 19°

Guida verificata passo dopo passo
1
Recall the cofunction identity for sine and cosine: \(\sin(\theta) = \cos(90^\circ - \theta)\).
Identify the angle in the given expression, which is \(19^\circ\) in \(\sin 19^\circ\).
Apply the cofunction identity by substituting \(\theta = 19^\circ\) into the formula: \(\sin 19^\circ = \cos(90^\circ - 19^\circ)\).
Simplify the expression inside the cosine function: \(90^\circ - 19^\circ = 71^\circ\).
Conclude that the cofunction with the same value as \(\sin 19^\circ\) is \(\cos 71^\circ\).

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:
1m

Concetti chiave

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

Trigonometric Cofunction Identity

Cofunction identities relate pairs of trigonometric functions whose angles add up to 90°. For example, sin(θ) equals cos(90° - θ). This means sin 19° can be expressed as cos(71°), since 19° + 71° = 90°.
Video consigliato:
Percorso guidato
6:30
Cofunction Identities

Sine Function

The sine function gives the ratio of the length of the side opposite an angle to the hypotenuse in a right triangle. It is periodic and ranges between -1 and 1, and is fundamental in relating angles to side lengths.
Video consigliato:
Percorso guidato
5:53
Graph of Sine and Cosine Function

Complementary Angles

Two angles are complementary if their sum is 90°. In trigonometry, complementary angles are important because the sine of one angle equals the cosine of its complement, enabling the use of cofunction identities.
Video consigliato:
Percorso guidato
3:35
Intro to Complementary & Supplementary Angles
Pratica correlata
Domanda del libro di testo

In Exercises 23–34, find the exact value of each of the remaining trigonometric functions of θ. tan θ = 4/3, cos θ < 0

593
views
Domanda del libro di testo

In Exercises 31–38, find a cofunction with the same value as the given expression. sin 7°

762
views
Domanda del libro di testo

In Exercises 29–34, convert each angle in degrees to radians. Round to two decimal places. -50°

577
views
Domanda del libro di testo

In Exercises 31–38, find a cofunction with the same value as the given expression. csc 25°

780
views
Domanda del libro di testo

In Exercises 25–32, 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 47𝜋/4

890
views
Domanda del libro di testo

In Exercises 23–34, find the exact value of each of the remaining trigonometric functions of θ. sec θ = -3, tan θ > 0

575
views