Sin cubed maybe?

Geometry Level 4

w = sin ⁡ 2 0 ∘ sin ⁡ 4 0 ∘ sin ⁡ 8 0 ∘ \large w = \sin 20^\circ \sin 40^\circ \sin 80^\circ

Find the closed form of w w .

Give your answer to 2 decimal places.


The answer is 0.22.

Dragan Marković by Dragan Marković , 26, Serbia

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

1 solution

Atul Kumar Ashish
Apr 28, 2016

sin20°•sin40°•sin80°.
=sin20°•sin(60°-20°)•sin(60°+20°).
Using sin(x+y)•sin(x-y)=sin²x-sin²y,
sin20°•{sin²60°-sin²20°}.
=sin20°•{3/4 - sin²20°}.
=(3sin20°-4sin³20°)/4.
=sin60°/4.
=√3/8 ≈ 0.22.


3 Helpful 0 Interesting 0 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...