Let's find the value of

`sin 18°∙sin 54°`without the calculator.

The things to remember are :

- The double angle formula for sine function, that is :
sin 2α = 2∙sin α∙cos α

- The co-function (0° ≤ α ≤ 90°), that is :
sin α = cos (90° - α) or cos α = sin (90° - α)

This brain teaser is actually an exercise in the section of sum of angles within the trigonometric function, especially for sine (double-angle) - senior high Math.

To "solve"sin 18°∙sin 54°, let's start fromsin 72°.

Why 72°?

It's from18° + 54° = 72°.

You'll see why I just added those two angles as the first step.

Look at this picture I made to watch where it will go :

Pretty much

**fun**. The answer is

**1/4**or

**0.25**.

This method only works for 18° and 54°. Both sine functions.

sin18°∙sin54°using co-function is equivalent withsin18°∙cos36°orcos72°∙sin54°orcos72°∙cos36°.

Anyway, I also made a JavaScript calculator for this particular post, for both sine functions, so you won't doubt the result above.

I round up the result to two decimal places. Try it out:

sin
°∙
sin
°

That is all. Thanks for visiting.

Related :

- List of trigonometric identities
- Basic trigonometric functions and special angles values, here at Monkey Raptor

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