SOLUTION: Find the exact value. (We are suppost to be using the trig addition and subtraction formulas to find a solution) For the first problem I got the answer -(√2)/2 and I got tot

Algebra ->  Formulas -> SOLUTION: Find the exact value. (We are suppost to be using the trig addition and subtraction formulas to find a solution) For the first problem I got the answer -(√2)/2 and I got tot      Log On


   

Question 148768: Find the exact value. (We are suppost to be using the trig addition and subtraction formulas to find a solution) For the first problem I got the answer -(√2)/2 and I got totally lost on the second problem. I'm not sure if my answer was correct. Help would be greatly appeciated. Thanks
1) sin(11pi/12) (use 11pi/12=2pi/3+pi/4)
2) tan(7pi/12) (use 7pi/12=3pi/4-pi/6)
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
I'll do the first one to get you started


sin%2811pi%2F12%29 ... Start with the given expression.


sin%282pi%2F3%2Bpi%2F4%29... Break up 11pi%2F12 to get 2pi%2F3%2Bpi%2F4.


sin%282pi%2F3%29cos%28pi%2F4%29%2Bcos%282pi%2F3%29sin%28pi%2F4%29 ... Use the "Sum-Difference" identities to rewrite the expression. Here's a good list of trig identities: http://www.sosmath.com/trig/Trig5/trig5/trig5.html


%28sqrt%283%29%2F2%29%28sqrt%282%29%2F2%29%2B%28-1%2F2%29%28sqrt%282%29%2F2%29 Take the sine of 2pi%2F3 to get sqrt%283%29%2F2. Take the cosine of pi%2F4 to get sqrt%282%29%2F2. Take the cosine of 2pi%2F3 to get -1%2F2. Finally, take the sine of pi%2F4 to get sqrt%282%29%2F2. If you aren't familiar with these values, use the unit circle.


sqrt%286%29%2F4-sqrt%282%29%2F4 Multiply.


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


So sin%2811pi%2F12%29=%28sqrt%286%29-sqrt%282%29%29%2F4


note: you can use a calculator to check your work.