Without drawing pictures or looking up the tables, arrange the numbers

Sin 1°, cos 1°, sin 2°, cos 2°

in ascending order.

Consider the angles :

sin 0°, cos 0°, sin 30°, cos 30°

We know that angles 0° and 30° lies in the same part of the graph of sin and cos where 1° and 2° lies.

∴ we can take the reference of them to arrange the other trigonometry angles which are counterpart of them.

Taking the values of the given trigonometry angles :

sin 0° = 0

cos 0° = 1

sin 30° = 0.5

cos 30° = 0.866

Arranging in ascending order :

⇒ sin 0° < sin 30° < cos 30° < cos 0°

Similarly,

⇒ sin 1° < sin 2° < cos 2° < cos 1°

Remember that we have taken 0° and 30° for comparison with 1° and 2° as the properties of sin and cos does not change in this range and they behave same as 1° and 2°.

sin 1° < sin 2° < cos 2° < cos 1°