CONCEPT PREVIEW  Fill in the blank(s) to correctly complete each sentence. Given tan θ = 1/cot θ , two equivalent forms of this identity are cot θ = 1/______ and tan θ . ______ = 1 .

Key Concepts

Reciprocal Identities

Reciprocal identities in trigonometry express the relationship between the primary trigonometric functions and their reciprocals. For example, the tangent function (tan θ) is the reciprocal of the cotangent function (cot θ), meaning tan θ = 1/cot θ. Understanding these identities is crucial for manipulating and solving trigonometric equations.

Trigonometric Functions

Trigonometric functions, including sine, cosine, tangent, cotangent, secant, and cosecant, are fundamental in trigonometry. Each function relates an angle of a right triangle to the ratios of its sides. Recognizing how these functions interrelate, such as tan θ and cot θ, is essential for solving problems involving angles and their measures.

Identity Verification

Identity verification in trigonometry involves proving that two expressions are equivalent for all values of the variable within a certain domain. This is often done by manipulating one side of the equation to match the other using known identities. Mastery of this concept allows students to confidently fill in blanks or complete identities in trigonometric equations.