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 26
Capitolo 3, Problema 26

Write each function in terms of its cofunction. Assume all angles involved are acute angles. See Example 2. tan 25.4°

Guida verificata passo dopo passo
1
Recall the cofunction identity for tangent: \( \tan(\theta) = \cot(90^\circ - \theta) \). This means the tangent of an angle is equal to the cotangent of its complement.
Identify the given angle \( \theta = 25.4^\circ \). Since the angles are acute, the complement is \( 90^\circ - 25.4^\circ \).
Calculate the complement angle: \( 90^\circ - 25.4^\circ = 64.6^\circ \).
Rewrite \( \tan 25.4^\circ \) using the cofunction identity as \( \cot 64.6^\circ \).
Thus, \( \tan 25.4^\circ \) expressed in terms of its cofunction is \( \cot 64.6^\circ \).

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 Functions

Trigonometric functions like sine, cosine, and tangent relate the angles of a right triangle to the ratios of its sides. Tangent of an angle is the ratio of the opposite side to the adjacent side. Understanding these functions is essential for manipulating and converting between them.
Video consigliato:
Percorso guidato
6:04
Introduction to Trigonometric Functions

Cofunction Identities

Cofunction identities express a trigonometric function of an angle in terms of the complementary angle's cofunction. For acute angles, tan(θ) = cot(90° - θ), meaning the tangent of an angle equals the cotangent of its complement. This relationship helps rewrite functions in terms of their cofunctions.
Video consigliato:
Percorso guidato
6:30
Cofunction Identities

Complementary Angles

Complementary angles are two angles whose measures add up to 90°. In trigonometry, many identities rely on this concept, especially cofunction identities. Recognizing that 25.4° and 64.6° are complementary allows rewriting tan 25.4° as cot 64.6°.
Video consigliato:
Percorso guidato
3:35
Intro to Complementary & Supplementary Angles
Pratica correlata
Domanda del libro di testo

Write each function in terms of its cofunction. Assume all angles involved are acute angles. See Example 2. cos(θ + 20°)

723
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. 495°

642
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. 1305°

714
views
Domanda del libro di testo

Write each function in terms of its cofunction. Assume all angles involved are acute angles. See Example 2. sin 45°

680
views
Domanda del libro di testo

Evaluate each expression. Give exact values. sec² 300° - 2 cos² 150°

656
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. B = 73.0°, b = 128 in.

621
views