# Van Schooten's Ruler Constructions - Trigonometry Exercises

Author(s):
C. Edward Sandifer

Here is a trig table based on a circle of radius 200. Angles are given in degrees. You can tell that the circle is of radius 200 because the table gives sin 90 as 200.

 Angle Sin Tan Sec 0 0 0 200 10 35 35 203 20 68 73 213 30 100 115 231 40 129 168 261 45 141 200 283 50 153 238 311 60 173 346 400 70 188 549 585 80 197 1134 1152 90 200

#### Questions

1. How does sin 90 = 200 tell you that the circle is of radius 200?

2. How can you use this table to get our modern value of sin 45, which we know to be about 0.701?

3. How can you use this table to get cosines?

4. In this table, is it still true that tan x = (sin x)/(cos x)?  How about sec x = 1/cos x?  Why or why not?

5. Suppose ABC is a right triangle with right angle at C, and that sides a, b, c are opposite angles A, B, C, respectively.  If b = 25 and if A = 40°, then use the table to find the length of side a.  You should not convert to modern values of sine and cosine.  In fact, it is better if you do not use any decimals, only fractions and whole numbers.

6. Suppose that ABC is a right triangle, with A = 20° and c = 40.  Find a.

##### Next:

Solutions to trigonometry exercises

Note to teachers

The other eight problems

Conclusions

C. Edward Sandifer, "Van Schooten's Ruler Constructions - Trigonometry Exercises," Loci (August 2010)