which is greater? sin 1 degee or sin 1^c(radian)?

Question

deals with trigonometry...

plz justify as well.

Answer 1

1 degree = 1 degree * pi/180 radian = pi/180 radian = 0.017453 radian

Since we know that the sin function only increases from 0 to pi/2, the larger a value in this interval, the larger the value of the sin. Therefore, since 1 radian > 0.017453 = 1 degree, the sin 1 radian > sin 1 degree.

sin 1 radian = 0.841471
sin 1 degree = 0.017452

thus showing than sin 1 radian > sin 1 degree!

Answer 2

1 degree=0.0174532925 radian
1 radian = 57.2957795 degree
it implies 1 degree < 1 radian
sin (0 degree)=0, sin (90 degree)=1
it implies sine value increases when its arguement increases.
so sin (1 degree) < sin (57.2957795 degree)
i.e sin (1 degree) < sin (1 radian) (because 57.2957795 degree=1 radian)

thus sin 1^c(radian) is greater than sin 1 degree....

Answer 3

Sin 1 degree is almost zero and is much smaller than sin 1 radian. A radian is 180/3.1416 = 57.29 degrees approx. It is closer to sin 60 which is sqrt3/2 = 0.8666..

So sin 1 rad is much much bigger than sin 1 deg.