Posted by T.Gracken on October 31, 2002 at 13:22:10:
In Reply to: Need help with headwrenching trig-equation! posted by Mikael Havel on October 31, 2002 at 11:51:06:
: I've been given what appears to be a simple problem, but it grows on me and I can't find any end to it!
: Define exactly
: sin(3x) + sin(5x)
: It follows that cos(x)=SQRT(8)/3
: and I've managed to sort out that
: sin(3x)=3sin(x)cos^2(x)-sin^3(x) and that this equals 23/27...
: sin(5x) however....
sin(5x) = sin(3x+2x)
you already know what sin(3x) is from above.
you can easily determine sin(2x) and cos(2x) from the double angle identities and the given.
note that from the given and your evaluation of sin(3x), the values of cos(x) and cos(3x) should also be relatively easy to determine...
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