Question

The greatest real number among sin1, sin2, sin3 and sin (√10 - 2) is

(A)  sin 1

(B)  sin 2 

(C)  sin 3

(D)  sin(√10 - 2)

Answer 1

Correct option (D)  sin(√10 - 2)

We know that sin x is an increasing function in [0,π/2]

Now,

sin 2 = sin (π − 2) = sin 1.14

sin 3 = sin (π − 3) = sin 0.14

sin(√10 - 2) = sin1.16

Therefore, among sin1, sin2, sin3 and sin (√10 - 2), sin(√10 - 2) is greatest.