Question

What is greater sin 1 rad or sin 2 rad?
Explain in brief your answer for the above.

Answer 1

The angle that is closer to \(\pi/2 \approx 1.57\) will have a greater sine.

Answer 2

Hint :

sin1 = sin(pi-1)
and (pi-1) > 2

Answer 3

Thats what I know.
But my teacher WANTS a more "precise" justification.

Answer 4

You also need to know that sinx is increasing for 0<x<pi/2
and decreasing for pi/2<x<pi

Answer 5

This is what I got:
1<1.57<2

Answer 6

First of all,
do you get why sin(1) equals sin(pi-1) ?

Answer 7

Perhaps drawing a unit circle might help

Answer 8

My teacher said I need to further explain :
1<1.57<2

Answer 9

Picking up on Parth's reply,

which is closer to 1.57,
1 or 2 ?

Answer 10

I know all of this.
I already did that

1.57 is close to 2 so sin 2 rad is greater .
But I need to write a more detailed explanation.

Answer 11

Imagine you're on a giant wheel