SOLUTION: Compute {{{ (sin 15+sin 75)^6 }}}

Algebra ->  Trigonometry-basics -> SOLUTION: Compute {{{ (sin 15+sin 75)^6 }}}      Log On


   

Question 1112841: Compute +%28sin+15%2Bsin+75%29%5E6+
Found 2 solutions by Alan3354, greenestamps:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Use a calculator.
==========
I don't see where I was being funny, or trying to be funny.
If you specify w/o using a calculator, then all the work is necessary.
If not, adding the 2 sines, then raising it to the 6th power gives 3.375, the same answer.
====================
Or,
sin%2815%29+=+%28sqrt%286%29+-+sqrt%282%29%29%2F4
sin%2875%29+=+%28sqrt%286%29+%2B+sqrt%282%29%29%2F4
sin%2815%29+%2B+sin%2875%29+=+sqrt%286%29%2F2
6th power --> 216/64 = 3.375
=============
Most people don't know the sine of 15 or 75 degs, tho.
Do you find that humorous?
PS The "funny bone" is at the end of the humerus.

Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


Sorry we have tutors here who think it is funny to provide useless answers to your real questions....

+%28sin+15%2Bsin+75%29%5E6+

= %28sin15%2Bcos15%29%5E6 (sinx = cos(90-x))

= %28%28sin15%2Bcos15%29%5E2%29%5E3

= %28%28sin15%29%5E2%2B2sin15cos15%2B%28cos15%29%5E2%29%5E3

= %281%2Bsin30%29%5E3 (sin^2+cos^2=1; 2sinxcosx = sin(2x))

= %283%2F2%29%5E3

= 27%2F8