Question

Can you help me? sin 35 (degrees) Thanks!

Answer 1

OK, here's a *very* approximate "creative" method: 

sin(a+b)=sin(a)cos(b) + cos(a)sin(b) 

choose a=30deg and b=5deg 
- sin(a)=0.5 (exact) 
- b is a small number so we say sin(b)~b (in radians). We can do a long division for this: 3.14/36 = 0.087 radians 
- similarly, for b sufficiently small, cos(b)~1 
- now we only need cos(a) = sqrt(3)/2. We can approximately calculate sqrt(3) as 1.73, (by trial-and-error or better, by using the Babylonian method;  so sqrt(3)/2 = 0.865 

Finally, sin(30 + 5) = (0.5 x 1) + (0.087 x 0.865) = 0.575 (calculating more digits is of no use because the sin(b)=b and cos(b)=1 are quite inaccurate approximations). 

So that wasn't all too much effort, and we're close to the correct answer (0.574)


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