Does commutative property apply?

Geometry Level 3

$A = \sin\left[\sin(1)\right] \\ B = \sin\left[\cos(1)\right] \\ C = \cos\left[\sin(1)\right] \\ D =\cos\left[\cos(1)\right]$

The above are the values of $A,B,C,$ and $D.$ Which of the answer choices is true?

Clarification: All angles are measured in radians.

Inspiration .

B < C< A < D

D < A < B < C

A < D < C < B

C < B < D < A

1 solution

Hitesh Yadav
Jul 14, 2020

Can do by doing back and forth between degrees and radians by approximating. $sin(sin(1))=sin(sin(57^{\circ} ))$ And then B was $sin(cos(1))$ which is the same way of saying $sin(cos(57^{\circ}))$ and since sine of 57 degrees is greater than cosine of 57 degrees thus A will be greater than B which is the case in only two options , namely option A and option D. And the only difference between the options is whether D is greater than or smaller than A. By applying the same methodology we can get the answer

Does commutative property apply?

1 solution

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