SOLUTION: Use the given information to find cos(x/2), sin(x/2), and tan(x/2). (Enter your answers in exact form.) csc x = 7, 0 < x < &#960;/2

Algebra ->  Trigonometry-basics -> SOLUTION: Use the given information to find cos(x/2), sin(x/2), and tan(x/2). (Enter your answers in exact form.) csc x = 7, 0 < x < &#960;/2       Log On


   

Question 965703: Use the given information to find cos(x/2), sin(x/2), and tan(x/2). (Enter your answers in exact form.)
csc x = 7, 0 < x < π/2
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
Use the given information to find cos(x/2), sin(x/2), and tan(x/2). (Enter your answers in exact form.)
csc x = 7, 0 < x < π/2
sin x=1/cscx=1/7
cosx=sqrt%281-sin%5E2%28x%29%29=sqrt%281-%281%2F49%29%29=sqrt%2848%2F49%29=sqrt%2848%29%2F7



check:
sinx=1/7
x=8.2132
x/2=4.1066
..
cos(x/2)=cos(4.1066)=0.9974
exact value as computed=sqrt%28%287%2Bsqrt%2848%29%29%2F14%29≈0.9974
..
sin(x/2)=sin(4.1066)=0.0716
exact value as computed=sqrt%28%287-sqrt%2848%29%29%2F14%29≈0.0714
..
tan(x/2)=tan(4.1066)=0.0718
exact value as computed=sqrt%287-sqrt%2848%29%29%2Fsqrt%287%2Bsqrt%2848%29%29
(let student check computed exact value)