Use identities to fill in each blank with the appropriate trigonometric function name.
tan 24° = 1/ _____ 66°

Key Concepts

Trigonometric Identities

Trigonometric identities are equations that involve trigonometric functions and are true for all values of the variables involved. They are essential for simplifying expressions and solving equations in trigonometry. Common identities include the Pythagorean identities, reciprocal identities, and co-function identities, which relate the functions of complementary angles.

Co-function Identity

Co-function identities state that the sine of an angle is equal to the cosine of its complement, and similarly for other functions. For example, sin(θ) = cos(90° - θ) and tan(θ) = cot(90° - θ). This concept is crucial for solving problems that involve angles that add up to 90 degrees, as seen in the given question.

Tangent and Cotangent Functions

The tangent function, tan(θ), is defined as the ratio of the opposite side to the adjacent side in a right triangle, while the cotangent function, cot(θ), is the reciprocal of tangent, or cot(θ) = 1/tan(θ). Understanding the relationship between these functions is vital for filling in the blank in the question, as it requires recognizing that tan(24°) relates to cot(66°) due to their complementary angles.