SOLUTION: Determine the exact value of the trigonometric functions listed below. cot (135) = is it -1? cos(pi/12)....where do I start?

Algebra ->  Trigonometry-basics -> SOLUTION: Determine the exact value of the trigonometric functions listed below. cot (135) = is it -1? cos(pi/12)....where do I start?      Log On


   

Question 84895: Determine the exact value of the trigonometric functions listed below.
cot (135) = is it -1?
cos(pi/12)....where do I start?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!


So you are correct cot+%28135%29=-1

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cos%28pi%2F12%29=cos%28pi%2F3-pi%2F4%29 Break up the argument. Note: pi%2F3-pi%2F4=4pi%2F12-3pi%2F12=1pi%2F12=pi%2F12

Now use the trig identity:
cos%28A-B%29=cos%28A%29cos%28B%29%2Bsin%28A%29sin%28B%29

cos%28pi%2F3-pi%2F4%29=cos%28pi%2F3%29cos%28pi%2F4%29%2Bsin%28pi%2F3%29sin%28pi%2F4%29 Plug in A=pi%2F3 and B=pi%2F4

Now using the unit circle, we get cos%28pi%2F3%29=1%2F2, cos%28pi%2F4%29=sqrt%282%29%2F2, sin%28pi%2F3%29=sqrt%283%29%2F2, and sin%28pi%2F3%29=sqrt%282%29%2F2


Substitute each trig function with it's corresponding expression


cos%28pi%2F3-pi%2F4%29=sqrt%282%29%2F4%2Bsqrt%286%29%2F4 Multiply

cos%28pi%2F3-pi%2F4%29=%28sqrt%282%29%2Bsqrt%286%29%29%2F4 Combine the fractions

So
cos%28pi%2F12%29=%28sqrt%282%29%2Bsqrt%286%29%29%2F4