Question

What is the equivalent trig ratio to cos 18 ?

Answer 1

Answer:

$\sin{72^\circ}$

Step-by-step explanation:

In a right triangle, the two acute angles are complementary--they add up to 90 degrees.

Cosine is defined as the adjacent side divided by the hypotenuse.  In the attached picture,  $\cos{18^\circ}=\frac{a}{h}$.

The other acute angle is 90 - 18 = 72 degrees.  Looking at just that angle, side a is the opposite side.  So the ratio a/h is opposite over hypotenuse -- the sine ratio.

Therefor, $\cos{18^\circ} = \sin{72^\circ}$