In Exercises 39–48, use a calculator to find the value of the trigonometric function to four decimal places. cot 𝜋 12

Key Concepts

Cotangent Function

The cotangent function, denoted as cot(θ), is the reciprocal of the tangent function. It is defined as cot(θ) = 1/tan(θ) or cot(θ) = cos(θ)/sin(θ). Understanding cotangent is essential for solving problems involving angles in trigonometry, especially when working with right triangles or unit circles.

Radians and Degrees

Trigonometric functions can be expressed in both radians and degrees. In this context, π/12 radians is equivalent to 15 degrees. It is crucial to know the unit of measurement being used, as calculators can be set to either mode, which affects the output of trigonometric functions.

Calculator Usage for Trigonometric Functions

Using a calculator to find trigonometric values requires familiarity with its functions and settings. To find cot(π/12), one must first calculate tan(π/12) and then take its reciprocal. Ensuring the calculator is in the correct mode (radians or degrees) is vital for obtaining accurate results.