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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)

Dummy View - NOT TO BE DELETED