Linear approximation of Tan(44)

[PsychStudent]

Homework Statement

Find the linear approximation of tan(44)

Homework Equations

f(x) = tan(44 + x), let x = a = 1
f`(x) = sec²(44+x)

The Attempt at a Solution

L(x) = f(a) + f`(a)(x-a)
L(x) = 1 + 2(x-1)
L(0) = 1 + 2(0-1) = -1 (Answer should be approx. 0.965)
Where am I going wrong? X should be zero, because tan(44+0) is what I'm trying to find the approximation of, right?

 

[Dick]

I think you want to find tan(44 degrees) by expanding tan(45+x) where x=(-1). But be careful about the derivatives when you are working in degrees. I think you are better off expanding tan(pi/4+x) (since pi/4=45 degrees) and then putting x=(-1) degrees, expressed in radians, of course.

 

[PsychStudent]

Well, that'll teach me never to use degrees again. It worked!

Thanks!

 

[Dick]

Yeah, degrees aren't fun. They just represent extra work.