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

Guida verificata passo dopo passo

Recall the cofunction identity for sine and cosine: \(\sin(\theta) = \cos(90^\circ - \theta)\) for acute angles.

Identify the given angle \(\theta = 45^\circ\).

Apply the cofunction identity by substituting \(\theta\) with \(45^\circ\): \(\sin(45^\circ) = \cos(90^\circ - 45^\circ)\).

Simplify the expression inside the cosine function: \(90^\circ - 45^\circ = 45^\circ\).

Write the final expression: \(\sin(45^\circ) = \cos(45^\circ)\).

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:

Concetti chiave

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

Trigonometric Functions

Trigonometric functions like sine, cosine, tangent, and their reciprocals relate the angles of a right triangle to the ratios of its sides. Understanding these functions is essential for expressing one function in terms of another, especially when dealing with complementary angles.

Video consigliato:

Percorso guidato

6:04

Introduction to Trigonometric Functions

Cofunction Identities

Cofunction identities state that the value of a trigonometric function of an angle equals the value of its cofunction at the complement of that angle. For example, sin(θ) = cos(90° - θ) for acute angles, which allows rewriting 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 and relationships, including cofunction identities, rely on this concept to connect functions of one angle to functions of its complement.

Video consigliato:

Percorso guidato