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April 17, 2014

April 17, 2014

Posted by **Anonymous** on Sunday, October 17, 2010 at 2:05am.

as 15 in the half angle formula used for calculating the value of sin 7.5 ?

- trig -
**Reiny**, Sunday, October 17, 2010 at 8:41amUnless 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

and using

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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