Find a calculator approximation to four decimal places for each circular function value. cos (-0.2443)

Verified step by step guidance

1. Recognize that the cosine function is even, meaning \( \cos(-x) = \cos(x) \). Therefore, \( \cos(-0.2443) = \cos(0.2443) \).
2. Use a calculator to find the cosine of the positive angle \( 0.2443 \) radians.
3. Ensure the calculator is set to radian mode, as the angle is given in radians.
4. Enter the value \( 0.2443 \) into the calculator and compute the cosine.
5. Round the result to four decimal places to obtain 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, cosine, and tangent, which are defined based on the unit circle. For any angle θ, the cosine function, cos(θ), represents the x-coordinate of the point on the unit circle corresponding to that angle.

Negative Angles

In trigonometry, negative angles indicate a clockwise rotation from the positive x-axis. The cosine function is an even function, meaning that cos(-θ) = cos(θ). This property allows us to simplify calculations involving negative angles by using their positive counterparts, making it easier to find values for functions like cos(-0.2443).

Calculator Approximations

Calculator approximations for trigonometric functions provide numerical values for angles that may not correspond to simple fractions or known values. Most scientific calculators can compute these values to a specified number of decimal places. For instance, finding cos(-0.2443) requires inputting the angle into the calculator and rounding the result to four decimal places for precision.