6.

Interpolation

a.

Interpolation is a method of estimating the value of functions of

angles which are not given in the tables, or estimating the angle, given the

function which is not listed in the tables. Briefly, it is a process that

assumes a straight-line difference between two values, such that the sine of

43,, 30' 30" has a value halfway between 43,, 30' and 43,, 31', and may be

found by adding one-half their difference to the function of 43,, 30'

EXAMPLE

Find the sine of 44,, 30' 40".

SOLUTION

Since the sine of 44,, 30' 40" is somewhere between the sine of 44,, 30' and

sine of 44,, 31', find the value of the latter functions and subtract the

value of sin 44,, 30' from the value of sin 44,, 31'.

The desired function is 40/60 or .67 of the one minute difference.

Therefore, .67 x .00021 = .00014

sin 44,, 30' 40" = .70091 + .000014 = .70105.

EXAMPLE

Find the cosine of 43,, 20' 20".

SOLUTION

Find and subtract the value of the function cos 43,, 21' from the value of

the function cos 43,, 20'.

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