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
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.
how to do the calculation while taking 'A'
as 15 in the half angle formula used for calculating the value of sin 7.5 ?
1 answer
1 answer