Question

Can cos30 is greater than cos3. Give easons

Answer 1

Answer:

Obviously NO

cos 30° is always lesser than cos 3°

consider the following triangles ( in the attachment),

In which AC=A'C'

cos 30°=AB/AC

cos 3° =A'B'/A'C'

From the figure it is clear that if angle increases then the value of adjacent side decreases,( as,BC is greater than B'C' and AC=A'C' by pythagoras theorem to have the hypotenuse of the triangles equal AB decreases and becomes lesser than A'B')

AB<A'C'

AB/AC<A'B'/A'C'

so, cos30°<cos3°

( in case of sin ,sin 30°> sin 3° as, BC is bigger)

Moverover value of cos decreases if angle increases.