Asked by Marcus
Use an appropriate local linear approximation to estimate the value of Cotangent 46 degrees.
Answers
Answered by
drwls
Use a Taylor series based at 45 degrees, and operate in radians for the derivative and the extra 1 degree.
cot 46 = cot 45 + d(cotx)/dx *(x - pi/4)
= cot 45 + d(cotx)/dx * pi/180
= 1 + (dcotx)/dx*(pi/180)
= 1 - csc^2(pi/4)*pi/180
= 1 - pi/90 = 0.9651
The exact answer is 0.96569
cot 46 = cot 45 + d(cotx)/dx *(x - pi/4)
= cot 45 + d(cotx)/dx * pi/180
= 1 + (dcotx)/dx*(pi/180)
= 1 - csc^2(pi/4)*pi/180
= 1 - pi/90 = 0.9651
The exact answer is 0.96569