SOLUTION: Determine an exact value for the expression {{sin pi/3 - cos 5 pi/6} divided by {1 - tan 3 pi/4 cot pi/4}} This is what i tried and got: {square root 3 - negative square root 3

Algebra ->  Trigonometry-basics -> SOLUTION: Determine an exact value for the expression {{sin pi/3 - cos 5 pi/6} divided by {1 - tan 3 pi/4 cot pi/4}} This is what i tried and got: {square root 3 - negative square root 3      Log On


   

Question 692226: Determine an exact value for the expression {{sin pi/3 - cos 5 pi/6} divided by {1 - tan 3 pi/4 cot pi/4}}
This is what i tried and got:
{square root 3 - negative square root 3/2} divided by {1- (-1)(1) = 3 multiplied by square root 3 divided by 1
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!

sin%28pi%2F3%29 pi%2F3 is a special angle. We should know that its sin is sqrt%283%29%2F2
cos+%285pi%2F6%29 5pi%2F6 is also special angle. (Any integer multiple of pi%2F6 is a special angle.) The reference angle is pi%2F6 and the cos of this is sqrt%283%29%2F2. Since 5pi%2F6 is in the second quadrant and cos is negative there, cos%285pi%2F6%29+=+-sqrt%283%29%2F2
tan%283pi%2F4%29 3pi%2F4 is also special angle. (Any integer multiple of pi%2F4 is a special angle.) The reference angle is pi%2F4 and the tan of this is 1. Since 3pi%2F4 is in the second quadrant and tan is negative there, tan%283pi%2F4%29+=+-1
cot%28pi%2F4%29 pi%2F4 is a special angle. We should know that its cot is 1.
Substituting in all these values into your expression we get:
%28%28sqrt%283%29%2F2%29-%28-sqrt%283%29%2F2%29%29%2F%281-%28-1%29%281%29%29%29
which simplifies as follows:
%28%28sqrt%283%29%2F2%29%2B%28sqrt%283%29%2F2%29%29%2F%281-%28-1%29%29%29
%28%282sqrt%283%29%2F2%29%2F2%29
%28%28cross%282%29sqrt%283%29%2Fcross%282%29%29%2F2%29
%28sqrt%283%29%2F2%29