Approximate value of sin 1 degree with complete explanation

Introduction
In trigonometry, the sine function is defined as the ratio of the length of the opposite side to the length of the hypotenuse in a right-angled triangle. The sine function is denoted by sin x, where x represents the angle in degrees or radians.

Calculation of sin 1 degree
To calculate the approximate value of sin 1 degree, we can use the Taylor series expansion of the sine function. The Taylor series expansion of sin x is given by:

sin x = x - x^3/3! + x^5/5! - x^7/7! + ...

By substituting x = 1 degree (π/180 radians), we get:

sin 1 degree ≈ 0.0174524064

Therefore, the approximate value of sin 1 degree is 0.0174524064.

Explanation
The Taylor series expansion of the sine function is an infinite series that converges for all values of x. The series is based on the fact that the sine function can be expressed as an infinite sum of powers of x. The series is truncated after a certain number of terms to obtain an approximate value of sin x.

In this case, we have used the first three terms of the series to calculate the approximate value of sin 1 degree. The error in this approximation is given by the next term in the series, which is very small and can be ignored for most practical purposes.

Conclusion
The approximate value of sin 1 degree is 0.0174524064. This value can be used in various trigonometric calculations involving small angles. It is important to note that this value is only an approximation and may not be accurate to many decimal places.