Question

the values of sinA and cosA are always less than 1.why?​

Answer 1

Answer:

THIS IS THE REASON WHY....

Step-by-step explanation:

The simple reason is that the length of the sides of a right triangle are always less than the length of the hypotenuse. So, the ratio of any side and hypotenuse is always less than 1. Now, in the case of 0 or 90 degree, the figure is no longer a triangle because one of the sides ceases to exist while the other side coincides with the hypotenuse. This is the reason that in these extreme cases, sin and cosine take values 0 or 1.

This explanation doesn't take into account the negative values. On a higher level, cosine and sine of an angle are defined respectively as the x and y co-ordinates of the point that you reach on a unit circle (with origin as center) by rotating through that angle. Since the circle is a unit circle with center at the origin, the co-ordinates on that circle can never be greater than 1 or less than -1.

Answer 2

1. sin
2. $sin(a) = \sqrt{1 - \cos {}^{2} (a) }$