What is the equivalent trig ratio to cos 18 ?

Mathematics

1 answer:

Anika [276]3 years ago

3 0

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 <em>a</em> is the opposite side. So the ratio a/h is opposite over hypotenuse -- the sine ratio.

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

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