Question 174439
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(75)=sin(45+30)}}} 



Remember, {{{sin(x+y)=sin(x)cos(y)+cos(x)sin(y)}}}



So this means that



{{{sin(75)=sin(45)cos(30)+cos(45)sin(30)}}}



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



{{{sin(75)=(sqrt(2)/2)(sqrt(3)/2)+(sqrt(2)/2)(1/2)}}}



Multiply



{{{sin(75)=sqrt(6)/4+sqrt(2)/4}}}




Combine the fractions.



{{{sin(75)=(sqrt(6)+sqrt(2))/4}}}




So the exact value of sin(75) is {{{(sqrt(6)+sqrt(2))/4}}}