SOLUTION: 1. Use the addition identity to find the exact value for sin 105°. Show the work using 60 degrees and 45 degrees

Algebra ->  Trigonometry-basics -> SOLUTION: 1. Use the addition identity to find the exact value for sin 105°. Show the work using 60 degrees and 45 degrees      Log On


   

Question 1205806: 1. Use the addition identity to find the exact value for sin 105°. Show the work using 60 degrees and 45 degrees
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!


sin+%28105%29°=sin+%2860%2B45%29°

Use the addition identity

sin%28alpha+%2Bbeta%29=sin%28alpha%29cos%28beta%29%2Bcos%28alpha%29sin%28beta%29

sin+%28105%29°=sin%2860%29cos%2845%29%2Bcos%2860%29sin%2845%29

sin+%28105%29°=%28sqrt%283%29%2F2%29%281%2Fsqrt%282%29%29%2B%281%2F2%29%281%2Fsqrt%282%29%29

sin+%28105%29°=sqrt%283%29%2F%282sqrt%282%29%29%2B1%2F%282sqrt%282%29%29.....rationalize
sin+%28105%29°=

sin+%28105%29°=sqrt%286%29%2F4%2Bsqrt%282%29%2F4

sin+%28105%29°=%28sqrt%286%29%2Bsqrt%282%29%29%2F4