SOLUTION: Find the exact value of sec(17л/12). PLEASE HELP ME!!!!!

Algebra ->  Trigonometry-basics -> SOLUTION: Find the exact value of sec(17л/12). PLEASE HELP ME!!!!!      Log On


   

Question 180774: Find the exact value of sec(17л/12). PLEASE HELP ME!!!!!
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!



sec%28%2817pi%29%2F12%29 Start with the given trig expression.


1%2F%28cos%28%2817pi%29%2F12%29%29 Use the identity sec%28A%29=1%2Fcos%28A%29


1%2F%28cos%28%287pi%29%2F6%2Bpi%2F4%29%29 Expand. Note: %2817pi%29%2F12=%287pi%29%2F6%2Bpi%2F4 (convert to degrees if that makes it easier to see)


1%2F%28cos%28%287pi%29%2F6%29cos%28pi%2F4%29-sin%28%287pi%29%2F6%29sin%28pi%2F4%29%29 Use the identity cos%28A%2BB%29=cos%28A%29cos%28B%29-sin%28A%29sin%28B%29 to expand



1%2F%28%28-sqrt%283%29%2F2%29cos%28pi%2F4%29-sin%28%287pi%29%2F6%29sin%28pi%2F4%29%29 Evaluate the cosine of %287pi%29%2F6 to get -sqrt%283%29%2F2 (use the unit circle)


1%2F%28%28-sqrt%283%29%2F2%29%28sqrt%282%29%2F2%29-sin%28%287pi%29%2F6%29sin%28pi%2F4%29%29 Evaluate the cosine of pi%2F4 to get sqrt%282%29%2F2 (use the unit circle)


1%2F%28%28-sqrt%283%29%2F2%29%28sqrt%282%29%2F2%29-%28-1%2F2%29sin%28pi%2F4%29%29 Evaluate the sine of %287pi%29%2F6 to get -1%2F2 (use the unit circle)



1%2F%28%28-sqrt%283%29%2F2%29%28sqrt%282%29%2F2%29-%28-1%2F2%29%28sqrt%282%29%2F2%29%29 Evaluate the sine of pi%2F4 to get sqrt%282%29%2F2 (use the unit circle)


1%2F%28-sqrt%286%29%2F4%2Bsqrt%282%29%2F4%29 Multiply


1%2F%28%28-sqrt%286%29%2Bsqrt%282%29%29%2F4%29 Combine the fractions.


1%2F%28%28sqrt%282%29-sqrt%286%29%29%2F4%29 Rearrange the terms.


%281%2F1%29%284%2F%28sqrt%282%29-sqrt%286%29%29%29 Multiply the first fraction (which is really 1%2F1) by the reciprocal of the second fraction


4%2F%28sqrt%282%29-sqrt%286%29%29 Multiply



=========================================================

Answer:


So sec%28%2817pi%29%2F12%29=4%2F%28sqrt%282%29-sqrt%286%29%29