SOLUTION: Find the exact value of sin (theta)/2 if cos (theta) = 2/3 and 270 deg. < (theta) < 360 deg.

Algebra ->  Trigonometry-basics -> SOLUTION: Find the exact value of sin (theta)/2 if cos (theta) = 2/3 and 270 deg. < (theta) < 360 deg.      Log On


   

Question 349082: Find the exact value of sin (theta)/2 if cos (theta) = 2/3 and 270 deg. < (theta) < 360 deg.
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
(For reasons I do not know, Algebra.com's formula software does not do theta, So I will be using alpha, alpha, instead.

The general formula is sin%28alpha%2F2%29+=+0+%2B-+sqrt%28%281-cos%28alpha%29%29%2F2%29
(The zero in front is due to another limitation of Algebra.com's software.)
Since alpha is between 270 and 360, sin is negative so we will use:
sin%28alpha%2F2%29+=+-+sqrt%28%281-cos%28alpha%29%29%2F2%29
Replacing cos%28alpha%29 with 2/3 we get:
sin%28alpha%2F2%29+=+-+sqrt%28%281-%282%2F3%29%29%2F2%29
Simplifying:
sin%28alpha%2F2%29+=+-+sqrt%28%283%2F3-%282%2F3%29%29%2F2%29
sin%28alpha%2F2%29+=+-+sqrt%28%281%2F3%29%2F2%29
sin%28alpha%2F2%29+=+-+sqrt%281%2F6%29
sin%28alpha%2F2%29+=+-+sqrt%28%281%2F6%29%286%2F6%29%29
sin%28alpha%2F2%29+=+-+sqrt%286%2F36%29
sin%28alpha%2F2%29+=+-+sqrt%286%29%2Fsqrt%2836%29
sin%28alpha%2F2%29+=+-+sqrt%286%29%2F6
which is the simplified, exact value for sin%28alpha%2F2%29.