Final answer:
The ratios 0 and 90 degrees in the Grade 10 CBSE syllabus are critical angles in trigonometry, important for understanding the properties of trigonometric functions, circles, and right-angled triangles. They are also significant in physics, such as calculating the projectile range, where the range is zero at 0 or 90 degrees.
Step-by-step explanation:
The significance of the ratios 0 and 90 in Grade 10 CBSE syllabus, particularly in relation to the reduced portion, can be most closely associated with trigonometry, one of the branches of mathematics. These ratios are directly linked to the foundational concepts of trigonometric functions and their properties. In trigonometry, 0 and 90 degrees are critical angles which correspond to specific values of sine, cosine, and tangent functions which are widely used to solve various geometric and physical problems. For instance, the sine of 0 degrees is 0 and the sine of 90 degrees is 1; whereas, the cosine of 0 degrees is 1 and of 90 degrees is 0. These ratios play a vital role in determining the values of other trigonometric functions and in understanding the properties of circles and right-angled triangles.
Answering the specific question given in the context of physics and the range of a projectile, the angle of projection for which the range is zero would be at angles where the horizontal component of the initial velocity is nil, which happens at angles of 0 or 90 degrees. The correct option is therefore 'c. 90° or 0°'.
In addition, these angles are also significant in other contexts like the calculation of celestial coordinates, the behavior of light when passing through polarizing filters, and the special conditions in Snell's law for critical angles. Hence, understanding the significance of 0 and 90 degrees is essential in both pure mathematics and its applications.