Knowing the angle between the directions from the Earth to the Moon and to the Sun, derive a formula that establishes the fraction of the Moon’s diameter perpendicular to the line connecting its horns and measures the width of the illuminated part of the Moon. Note: Directions to the Sun from the Earth and from the Moon are considered parallel (they differ by less than 9 ‘).
If the Moon L is visible in the form of a crescent, then the angle a at the Earth T between the directions on it and on the Sun S is less than 90 °. Having built the drawing, we see that the desired value is x = 1 / 2- 1/2 cos a = sin ^ 2 * f / 2. , if the diameter of the moon is taken as 1.
Remember: The process of learning a person lasts a lifetime. The value of the same knowledge for different people may be different, it is determined by their individual characteristics and needs. Therefore, knowledge is always needed at any age and position.