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

Verified step by step guidance

1. Recall the cofunction identity: \( \cos(\theta) = \sin\left(\frac{\pi}{2} - \theta\right) \).
2. Identify \( \theta \) in the given expression: \( \theta = \frac{3\pi}{8} \).
3. Substitute \( \theta \) into the cofunction identity: \( \cos\left(\frac{3\pi}{8}\right) = \sin\left(\frac{\pi}{2} - \frac{3\pi}{8}\right) \).
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. Conclude that the cofunction with the same value is \( \sin\left(\frac{\pi}{8}\right) \).

Key Concepts

Cofunction Identities

Cofunction identities in trigonometry relate the values of trigonometric functions of complementary angles. For example, the sine of an angle is equal to the cosine of its complement: sin(θ) = cos(90° - θ). This concept is essential for finding cofunctions, as it allows us to express one function in terms of another based on their complementary relationship.

Unit Circle

The unit circle is a fundamental concept in trigonometry that defines the values of sine and cosine for various angles. It is a circle with a radius of one centered at the origin of a coordinate plane. Understanding the unit circle helps in visualizing and calculating the values of trigonometric functions, including identifying cofunctions at specific angles.

Angle Measurement

Angle measurement in trigonometry can be expressed in degrees or radians. The expression cos(3π/8) uses radians, where π radians equals 180 degrees. Knowing how to convert between these two systems is crucial for solving trigonometric problems, especially when determining cofunctions or evaluating expressions at specific angles.