Radian V/S Degree

Geometry Level 3

Compare the following inequalities:

a) $\cos 1 < \cos 1^\circ$
b) $\sin 1 > \sin 1^\circ$
c) $\sin 1^\circ< \sin 2^\circ$
d) $\sin 2 > \sin3$
e) $\cos 1 > \sin1$

How many of these inequalities above are true?

Bonus : Solve this question using graph.

None of the them 1 3 4 5 2

1 solution

Nelson Mandela
Aug 29, 2015

A,B,C,D are true.

A- as cos is a decreasing function(in 0 to pi/2), cos1 degree < cos1(radian = 57.3 degrees).

B- As sine is an increasing function(in 0 to pi/2), sin1>sin 1 degree.

C- As sine is an increasing function(in 0 to pi/2),sin2 degrees> sin1 degree.

D- Sin2(sin114 = sin67) > Sin3(sin171 = sin9) as sine is an increasing function(in 0 to pi/2).

E- FALSE. As in (pi/4 to 3pi/4) sine curve dominates over cos curve. So, cos1<sin1.

So, no.of. true statements = 4.