SOLUTION: Use half-angle formulas to find the exact values. cos 165° I got {{{sqrt(2+{{{(sqrt3)}}}/2 which is wrong. This is my work: 165=θ/2 330= θ cos θ/2= {{{sqrt(1+co

Algebra ->  Trigonometry-basics -> SOLUTION: Use half-angle formulas to find the exact values. cos 165° I got {{{sqrt(2+{{{(sqrt3)}}}/2 which is wrong. This is my work: 165=θ/2 330= θ cos θ/2= {{{sqrt(1+co      Log On


   

Question 1159668: Use half-angle formulas to find the exact values.
cos 165°
I got sqrt%282%2B%7B%7B%7B%28sqrt3%29/2 which is wrong.
This is my work:
165=θ/2
330= θ
cos θ/2= sqrt%281%2Bcos+%CE%B8%29/2= sqrt%28%281%2B%28%7B%7B%7Bsqrt%283%29/2)/2)}}}}}}= sqrt%282%2B%7B%7B%7B%28sqrt3%29}}}/2
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!


cos%28A%2F2%29=± sqrt%28%281%2Bcos%28A%29%29%2F2%29
If A%2F2 is in the first or fourth quadrants, the formula uses the positive case:
If A%2F2+is in the second or third quadrants, the formula uses the negative case:
in your case angle is A%2F2=165°-> the second quadrant

if A%2F2=165°, ->A=330°


cos%28165%29=-sqrt%28%281%2Bcos%28330%29%29%2F2%29
cos%28165%29=-sqrt%281%2F2+%281+%2B+sqrt%283%29%2F2%29%29
cos%28165%29=-sqrt%28+%281+%2B+sqrt%283%29%2F4%29%29
cos%28165%29=-sqrt%282+%2B+sqrt%283%29%29%2F2
cos%28165%29=-%281+%2B+sqrt%283%29%29%2F%282sqrt%282%29%29