SOLUTION: 6. true or false: it is not possible to find the exact value of sin75? if fals efind exact value

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Question 174439: 6. true or false: it is not possible to find the exact value of sin75? if fals efind exact value
Answer by jim_thompson5910(21667) About Me  (Show Source):
You can put this solution on YOUR website!
False. It is possible to find the exact value of sin(75), and here's how:


First, break up 75 into 45+30 (which are known angles on the unit circle)


sin%2875%29=sin%2845%2B30%29


Remember, sin%28x%2By%29=sin%28x%29cos%28y%29%2Bcos%28x%29sin%28y%29


So this means that


sin%2875%29=sin%2845%29cos%2830%29%2Bcos%2845%29sin%2830%29


Evaluate each trig function (by use of the unit circle)


sin%2875%29=%28sqrt%282%29%2F2%29%28sqrt%283%29%2F2%29%2B%28sqrt%282%29%2F2%29%281%2F2%29


Multiply


sin%2875%29=sqrt%286%29%2F4%2Bsqrt%282%29%2F4



Combine the fractions.


sin%2875%29=%28sqrt%286%29%2Bsqrt%282%29%29%2F4



So the exact value of sin(75) is %28sqrt%286%29%2Bsqrt%282%29%29%2F4