In Exercises 31–38, find a cofunction with the same value as the given expression. tan 𝜋 9

Key Concepts

Cofunction Identities

Cofunction identities relate the trigonometric functions of complementary angles. For example, the sine of an angle is equal to the cosine of its complement, and vice versa. This means that for any angle θ, sin(θ) = cos(90° - θ) and tan(θ) = cot(90° - θ). Understanding these identities is crucial for finding cofunctions with the same value.

Tangent Function

The tangent function, defined as the ratio of the sine and cosine functions (tan(θ) = sin(θ)/cos(θ)), is periodic and has specific values at key angles. It is important to know the values of the tangent function at standard angles (like 0°, 30°, 45°, 60°, and 90°) to effectively evaluate expressions and find cofunctions. In this case, tan(π/9) is the expression we need to analyze.

Angle Measurement in Radians

In trigonometry, angles can be measured in degrees or radians, with radians being the standard unit in most mathematical contexts. The angle π/9 radians corresponds to 20° (since π radians equals 180°). Understanding how to convert between these two systems is essential for evaluating trigonometric functions and applying cofunction identities correctly.