Question

Apporoximate value of sin(29 degree 30 minutes

Answer 1

Answer:

0.87475

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Answer 2

Answer:

       sin( 29.5° )  ≈  1/2  -  π√3 / 720  ≈  0.49244250

Step-by-step explanation:

A linear approximation around 30° looks like a good option here.

For a function f(x) and a small change h in the value of x, we have...

• f'(x)  ≈  ( f(x+h) - f(x) ) / h             [ here, f'(x) is the derivative of f(x) ]

And so...

• f(x+h)  ≈  f(x) + f'(x).h

We want to use this with f(x) = sin x, x = 30° and h = -30 minutes = -0.5°.

Then f'(x) = cos x.

Also, we need to work with radians for these functions, so use

• x = 30° = π/6 radians
• h = -0.5° = -(0.5π)/180 = -π/360 radians

Now for the approximation:

    sin( 29.5° ) = sin( 30° - 0.5° ) = sin( π/6 - π/360 )

≈  sin( π/6 )  +  cos( π/6 ) × ( -π/360 )

=  1/2  -  √3/2 × π/360

= 1/2  -  π√3 / 720

To 8 decimal places, this approximation is

  sin( 29.5° )  ≈  0.49244250

while the correct value would be (to 8 decimal places)

  sin( 29.5° )  =  0.49242356...

Hope this helps.