Find a calculator approximation to four decimal places for each circular function value. See Example 3. tan 4.0203

Verified step by step guidance

1. Identify the trigonometric function you need to evaluate, which is \( \tan(4.0203) \).
2. Ensure your calculator is set to the correct mode (radians or degrees). Since 4.0203 is a radian measure, set your calculator to radians.
3. Enter the value 4.0203 into your calculator.
4. Use the tangent function key to calculate \( \tan(4.0203) \).
5. Round the result to four decimal places to get the final approximation.

Key Concepts

Circular Functions

Circular functions, also known as trigonometric functions, relate the angles of a circle to the ratios of its sides. The primary circular functions include sine (sin), cosine (cos), and tangent (tan). These functions are periodic and are defined for all real numbers, with their values derived from the unit circle, where the angle corresponds to a point on the circle.

Calculator Approximations

Calculator approximations involve using a scientific or graphing calculator to compute the values of trigonometric functions for given angles. These calculators typically provide results in decimal form, allowing for precise evaluations of functions like tan, sin, and cos. When approximating to a specific number of decimal places, it is essential to round correctly based on standard mathematical rules.

Radian Measure

Radian measure is a way of measuring angles based on the radius of a circle. One radian is the angle formed when the arc length is equal to the radius of the circle. In trigonometry, angles can be expressed in radians or degrees, and many calculators default to radians for trigonometric functions. Understanding how to convert between these two measures is crucial for accurate calculations.