Plane trigonometry, by S.L. Loney.

CIRCULAR MEASURE.

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(3) Since 1050~ = 11 x 90~ + 60~, the revolving line has turned through
60~ more than eleven right angles and is therefore between OB' and OA
and makes 60~ with OB'.
EXAMPLES. I.
Express in terms of a right angle the angles
1. 60~. 2. 75~ 15'. 3. 63~ 17'25".
4. 130~ 30'. 5, 210 30'30". 6. 370020'48".
Express in grades, minutes, and seconds the angles
7. 30~. -8. 810. 9. 138~ 30'. 10. 350 47'15".
11. 235~ 12' 36". 12. 475 13'48".
Express in terms of right angles and also in degrees, minutes, and
seconds the angles
13. 120g. 14. 45g 35' 24'. 15. 39g45'36".
16. 255s48' 81". 17. 759g 45' 60".
Mark the position of the revolving line when it has traced out the
following angles:
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18. - right angle. 19. 3~ right angles. 20. 131 right angles.
21. 120~. 22. 315~. 23. 745~. 24. 1185~. 25. 150g.
26. 420g. 27. 875g.
28. How many degrees, minutes and seconds are respectively passed
over in 11-I minutes by the hour and minute hands of a watch?
29. The number of degrees in one acute angle of a right-angled
triangle is equal to the number of grades in the other; express both the
angles in degrees.
30. Prove that the number of Sexagesimal minutes in any angle is
to the number of Centesimal minutes in the same angle as 27: 50.
31. Divide 44~ 8' into two parts such that the number of Sexagesimal
seconds in one part may be equal to the number of Centesimal seconds in
the other part.
Circular Measure.
9. A third system of measurement of angles has
been devised, and it is this system which is used in all
the higher branches of Mathematics.