Posted by Anonymous on Sunday, October 17, 2010 at 2:05am.
how to do the calculation while taking 'A'
as 15 in the half angle formula used for calculating the value of sin 7.5 ?
trig - Reiny, Sunday, October 17, 2010 at 8:41am
Unless you have found sin15 or cos15 before, and it has become part of your trig repertoire , you will have to do it twice
since you must know that cos 30 = √3/2
cos 2A = 2cos^2 A - 1 , let 2A = 30
cos30 = 2cos^2 15 - 1
solving this for cos 15 I got √(√3 + 2)/2
now use the other expansion for cos 2A
cos 2A = 1 - 2sin^2 A
cos 15 = 1 - 2sin^2 7.5
this gave me
2sin^2 7.5 = 1 - √(√3 + 2)/2
sin 7.5 = √[2 - √(√3 + 2) ]/2
you can check it with sin 7.5 on your calculator, it is correct.
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