Question

the value of sin A and cos A is always less than 1 why?

Answer 1

We know that,
$sina = \frac{perpendicular}{hypotenuse} and \: cosa = \frac{base}{hypotenuse} \\ also \: hypotenuse \: is \: the \: longest \: side \\ that \: means \: whenever \: you \: find \: sina \: or \: cosa \: you \: divide \: a \: value \: by \: bigger \: value \: and \: hence \: you \: get \: the \: value \: less \: than \: one \\ eg \: consider \: \: right triangle \: such \: that \: perpendicular = 4 \: base = 3 \: then \: hypotenuse = 5 \\ so \: when \: u \: find \: sina \: u \: have \: to \: divide \: 4 \: by \: 5 \: which \: comes \: out \: to \: be \: 0.8 \: which \: is \: less \: than \: 1 \: and \: same \: is \: with \: cosa \\ always \: remember \: one \: rule \: that \: if \: z = \frac{x}{y} such \: that \: x < y \: then \: z < 1 \\ this \: rule \: is \: applicable \: in \: this \: question \: also \: and \: hence \: u \: get \: value \: less \: than \: 1$
hope this would help!!

Answer 2

Answer:

hey !!

Step-by-step explanation:

The value of sin as well as Cos function is always less than 1 because of its definition that for a right triangle, the sine is the opposite side divided by the hypotenuse.  And we know Hypotenuse is longest side in any right angle triangle.

Similarly for cos, therefore the function are less than 1.