Approximating cos(47∘) Given that cos(45∘)=22 what would cos(47∘) be. Using differential approximation, I get cos(47∘)...
Given that what would be.
Using differential approximation, I get is about which is of course not right as
Answer & Explanation
When you write (dropping the minus sign) you need to measure in radians. That comes out in your formula in the times 2, which should be times . So
Check your units. The general form for differential approximation is
You convert your 47, which I'm assuming is in degrees to radians by multiplying by . This is fine. But then you use 2 degrees (I'm assuming) as your term. You need this to be in radians.
Try your computation again, using the same method you've already used to convert from degrees to radians for 2 degrees. The answer you then get is off by about 0.004. But I'll leave it to you to check which way it is off