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

Verified step by step guidance

1. Recall the cofunction identity for cosine and sine: \(\cos(\theta) = \sin\left(\frac{\pi}{2} - \theta\right)\).
2. Identify the angle \(\theta\) in the given expression, which is \(\frac{3\pi}{8}\).
3. Substitute \(\theta = \frac{3\pi}{8}\) into the cofunction identity to get \(\cos\left(\frac{3\pi}{8}\right) = \sin\left(\frac{\pi}{2} - \frac{3\pi}{8}\right)\).
4. Simplify the expression inside the sine function: \(\frac{\pi}{2} - \frac{3\pi}{8} = \frac{4\pi}{8} - \frac{3\pi}{8} = \frac{\pi}{8}\).
5. Write the final cofunction expression: \(\cos\left(\frac{3\pi}{8}\right) = \sin\left(\frac{\pi}{8}\right)\).

Key Concepts

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.

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.

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.