A unitless number with a value from 0 to 1 is called

A unitless number with a value from 0 to 1 is called

• A. Angle
• B. Sine
• C. Cosine
• D. Tangent

Answer: (B)

A unitless number from 0 to 1 is what you get from a trigonometric ratio, specifically the sine of an angle. Sine is defined as the opposite side length divided by the hypotenuse in a right triangle, and because it’s a ratio of lengths, the units cancel, leaving a pure number. For angles in the first quadrant (0 to 90 degrees), that ratio cannot exceed 1 and varies from 0 up to 1 as the angle goes from 0 to 90 degrees. So sine naturally fits the description of a unitless value between 0 and 1. The other options aren’t a perfect fit: an angle isn’t a ratio, tangent can be any real number (not restricted to 0–1), and cosine is also a ratio that lies between 0 and 1 for acute angles but the standard example described by this phrase is sine.

A unitless number from 0 to 1 is what you get from a trigonometric ratio, specifically the sine of an angle. Sine is defined as the opposite side length divided by the hypotenuse in a right triangle, and because it’s a ratio of lengths, the units cancel, leaving a pure number. For angles in the first quadrant (0 to 90 degrees), that ratio cannot exceed 1 and varies from 0 up to 1 as the angle goes from 0 to 90 degrees. So sine naturally fits the description of a unitless value between 0 and 1. The other options aren’t a perfect fit: an angle isn’t a ratio, tangent can be any real number (not restricted to 0–1), and cosine is also a ratio that lies between 0 and 1 for acute angles but the standard example described by this phrase is sine.