Sine and Cosine are defined as the ratios of sides of a right-angle triangle.
The denominator in the ratio is the hypotenuse of the triangle and the numerator is one of the other sides of the same triangle.
The hypotenuse (denominator of the fraction) is always longer than the other sides of the right triangle, therefore their fractions are always smaller than 1.
* The values of sine and cosine are coordinates of points on the unit circle.
* Coordinates of a point are always less than or equal to (in magnitude) their distance from the origin.
* Points on the unit circle are exactly one unit from the origin.
Therefore, the values of sine and cosine must be less in magnitude than one.
Latest Answers