Approximating cos⁡(47∘) Given that cos⁡(45∘)=22 what would cos⁡(47∘) be. Using differential approximation, I get cos⁡(47∘)...

Kaydence Huff

Kaydence Huff

Answered

2022-01-27

Approximating cos(47)
Given that cos(45)=22 what would cos(47) be.
Using differential approximation, I get cos(47) is about cos(45π180)2sin(47π180)=0.755600622 which is of course not right as cos(47)=0.68199836

Answer & Explanation

Eleanor Shaffer

Eleanor Shaffer

Expert

2022-01-28Added 16 answers

When you write cos(θ)=sin(θ) (dropping the minus sign) you need to measure θ in radians. That comes out in your formula in the times 2, which should be times 2π180. So
cos(47)cos(45)2π180sin(45)22(10.035)0.682
Eleanor Shaffer

Eleanor Shaffer

Expert

2022-01-29Added 16 answers

Check your units. The general form for differential approximation is
f(x0)+(xx0)ddxf
You convert your 47, which I'm assuming is in degrees to radians by multiplying by π180. This is fine. But then you use 2 degrees (I'm assuming) as your xx0 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 (±)

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