Ch. 1 - Angles and the Trigonometric Functions

Blitzer3rd EditionTrigonometryISBN: 9780137316601Non è quello che usi tu?Cambia libro di testo

Blitzer 3rd Edition

Ch. 1 - Angles and the Trigonometric Functions

Problema 38

Capitolo 1, Problema 38

Find a cofunction with the same value as the given expression.
cos (3𝜋/8)

Guida verificata passo dopo passo

Recall the cofunction identity for cosine and sine: \(\cos(\theta) = \sin\left(\frac{\pi}{2} - \theta\right)\).

Identify the angle \(\theta\) in the given expression, which is \(\frac{3\pi}{8}\).

Substitute \(\theta = \frac{3\pi}{8}\) into the cofunction identity to get \(\cos\left(\frac{3\pi}{8}\right) = \sin\left(\frac{\pi}{2} - \frac{3\pi}{8}\right)\).

Simplify the expression inside the sine function: \(\frac{\pi}{2} - \frac{3\pi}{8} = \frac{4\pi}{8} - \frac{3\pi}{8} = \frac{\pi}{8}\).

Write the final cofunction expression: \(\cos\left(\frac{3\pi}{8}\right) = \sin\left(\frac{\pi}{8}\right)\).

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Cofunction Identities

Cofunction identities relate the trigonometric functions of complementary angles, such as sin(θ) = cos(π/2 - θ). These identities allow us to express one trigonometric function in terms of another by using the complementary angle, which is essential for finding equivalent expressions.

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Percorso guidato

6:30

Cofunction Identities

Complementary Angles

Complementary angles are two angles whose measures add up to π/2 radians (90 degrees). Understanding this concept is crucial because cofunction identities depend on the relationship between an angle and its complement to simplify or rewrite trigonometric expressions.

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Intro to Complementary & Supplementary Angles

Evaluating Trigonometric Expressions in Radians

Trigonometric functions often use radian measure, where π radians equal 180 degrees. Being comfortable converting and interpreting angles in radians, such as 3π/8, helps in applying identities and finding equivalent expressions accurately.

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5:04

Converting between Degrees & Radians

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