If θ is an acute angle and cos θ = 1/3, find csc (𝜋/2 - θ).

Key Concepts

Trigonometric Functions

Trigonometric functions relate the angles of a triangle to the lengths of its sides. The primary functions include sine, cosine, and tangent, which are defined for acute angles in a right triangle. Understanding these functions is essential for solving problems involving angles and their relationships.

Cofunction Identity

Cofunction identities express the relationship between the sine and cosine of complementary angles. Specifically, csc(π/2 - θ) is equal to sin(θ). This identity is crucial for transforming expressions involving trigonometric functions and simplifying calculations.

Reciprocal Functions

Reciprocal functions in trigonometry include cosecant (csc), secant (sec), and cotangent (cot), which are the reciprocals of sine, cosine, and tangent, respectively. For example, csc(θ) = 1/sin(θ). Recognizing these relationships helps in finding values of trigonometric functions based on known values.