Thread: What is the exact value of sin 12 degrees?

What is the exact value of sin 12 degrees?

Only hint I was given was to use compound angle formula. Had this on the test but I left it blank, now I just want to know the solution.

Originally Posted by ISeriouslyNeedHelp

What is the exact value of sin 12 degrees?

Only hint I was given was to use compound angle formula. Had this on the test but I left it blank, now I just want to know the solution.

12 degrees is

so one way to do this is to use



divide up into U and V

for example

then use the difference formula...

can you take it from there??

Originally Posted by bigwave

12 degrees is

so one way to do this is to use



divide up into U and V

for example

then use the difference formula...

can you take it from there??

Now of course there's the new problem of finding and ....

I suspect there's more to the original question than was posted.

There is nothing more to this question. It is simply to find the exact value of sin 12 degrees. Only thing I could think of was sin(60/5), but these odd numbers really mess with my head.

Originally Posted by ISeriouslyNeedHelp

What is the exact value of sin 12 degrees?

Only hint I was given was to use compound angle formula. Had this on the test but I left it blank, now I just want to know the solution.

To do this you need:



We know the values of the trig functions for and so if we also know the trig function values for we are home and dry.

We can get the values we need for the and of from the geometry of a regular pentagon (which we could have guessed as we are dealing with integer fractions of , where we find:



where is the Golden number.

CB