Find a calculator approximation to four decimal places for each circular function value.
sin 1.0472

Verified step by step guidance

1. Identify the angle given in radians: 1.0472.
2. Recognize that the problem asks for the sine of this angle.
3. Use a scientific calculator to find the sine of 1.0472 radians.
4. Ensure the calculator is set to radian mode, not degree mode.
5. Read the calculator's output and round the result to four decimal places.

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 a unit circle. For example, the sine of an angle is the y-coordinate of the point on the unit circle corresponding to that angle.

Radians and Degrees

Angles can be measured in degrees or radians, with radians being the standard unit in trigonometry. One radian is the angle formed when the arc length is equal to the radius of the circle. The angle 1.0472 radians is approximately 60 degrees, which is significant for calculating trigonometric values.

Calculator Approximations

Calculator approximations involve using a scientific calculator to compute the values of trigonometric functions to a specified degree of accuracy. For instance, when finding sin(1.0472), the calculator provides a decimal approximation, which can be rounded to four decimal places for precision in applications.