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Linear Approximation??????
sin 59
so far i got
sin 59 is about sin 60....
so (rad2/2)-dy is the equation
then you differenciate sinx
you get
dy=cos 60 dx
dx=x final- x initial
so dx= 60-59
dx=1
here is my issue if dx= 1
then plugging it back in dy=cos 60 (1)......dy=1/2
rad 2/2-.5=.207
and sin(59)=.6367
Ideas?
1 Answer
- kbLv 71 decade agoFavorite Answer
The trigonometric formulas in Calculus work in radian measure nicely.
59 degrees --> 59π/180 (radians).
Note that π/3 (60 degrees) is close to 59π/180.
So, let's find the linear approximation of y = sin x at x = π/3.
Point: (π/3, √3/2).
Slope: y' = cos x {at x = π/3} = 1/2.
==> y - √3/2 = (1/2)(x - π/3).
So, the tangent line is y = √3/2 + (1/2)(x - π/3).
For points near x = π/3, the tangent line will give a good approximation.
So, sin x ≈ √3/2 + (1/2)(x - π/3).
==> sin(59π/180) ≈ √3/2 + (1/2)(59π/180 - π/3) ≈ 0.8573.
I hope this helps!
