Let's find the value of sin 18°∙sin 54° without the calculator.
Before we start...
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The double angle formula for sine function is: sin 2α = 2∙sin α∙cos α -
The co-function (0° ≤ α ≤ 90°) is: sin α = cos (90° - α)Or: cos α = sin (90° - α)
This is a brain teaser for sum of angles in the trigonometric function, especially for sine (double-angle) — senior high school math.
To solve sin 18°∙sin 54°, we can magically start from sin 72°
Why 72°? 🤔
Because... 18° + 54° = 72°
And... 72 ➗ 2 = 36
72 is 36 being doubled.
It fits our theme, double-angle 💡
The magic is revealed 🪄
🧙♂️
We will see how the addition above will solve the problem.
This is the image of the steps:
The answer is ¼ 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°.
This is an application for this particular post, for both sine functions, so we can prove the result from the steps above.
The output is rounded up to two decimal places.
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