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.

reading.

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