f. Suppose you wanted to find the sine 21 12' 20". Since Figure 4-5 shows only the
one-third of the way from 21 12' 00" to 21€ 13' 00", whose functions can be obtained from Figure 4-5.
By the principle of proportional parts discussed in the previous paragraph, an increase of 20" in the
angle 21€ 12' causes one-third as much change in its sine as is caused by an increase of 1 minute in the
angle.
Figure 4-5. Interpolation
Example: Find the value of sine 21 12' 20". The stated value of any angle is known as its tabular
reading.
Solutions:
First Method: Set up the ratio.
sin 21€ 13'= 0.36190
sin 21€ 12'= 0.36162
0.00028 difference
Therefore: sin 21€ 12'= 0.36162
By interpolation: 20"= 9
Then: sin 21 12' 20" = 0.36171
EN0591
4-12
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