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 from sin 72°.
It's from 18° + 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 with sin18°∙cos36° or cos72°∙sin54° or cos72°∙cos36°.
I round up the result to two decimal places. Try it out:
sin °∙ sin °
That is all. Thanks for visiting.