By Isaac Todhunter

This Elibron Classics ebook is a facsimile reprint of a 1864 variation through Macmillan and Co., Cambridge and London.

**Read or Download A Treatise On The Differential Calculus with numerous examples PDF**

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**Extra info for A Treatise On The Differential Calculus with numerous examples**

**Sample text**

Also classify each as equilateral, isosceles, or scalene. See the discussion following Example 2. 25. 26. 27. 60° 8 8 120° 60° 60° 8 28. 29. 30. 3 8 90° 9 130° 9 4 5 8 6 31. 32. 33. 4 10 96° 14 4 60° 34. 35. 36. 60° r 13 5 90° r 12 50° 50° 60° 60° r 9 37. Write a definition of isosceles right triangle. 9 38. Explain why the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. 2 Angle Relationships and Similar Triangles 9 39. Use this figure to discuss why the measures of P the angles of a triangle must add up to the same sum as the measure of a straight angle.

Source: Hamilton, J. E. and M. S. ) 2 5 n Q T m and n are parallel. 60° Point marked on line Tip placed here “Draw a straight line segment, and mark a point near the midpoint. Now place the tip on the marked point, and draw a semicircle. Without changing the setting of the pair of compasses, place the tip at the right intersection of the line and the semicircle, and then mark a small arc across the semicircle. Finally, draw a line segment from the marked point on the original segment to the point where the arc crosses the semicircle.

Cot u, given that tan u = 18 7. cos u, given that sec u = 9. sin u, given that csc u = 5 2 28 2 8. cos u, given that sec u = - 11 7 10. sin u, given that csc u = 224 3 11. 5 12. 01 13. 42716321 14. 80425133 9 15. Can a given angle u satisfy both sin u 7 0 and csc u 6 0 ? Explain. 9 16. ” 2 17. Concept Check What is wrong with the following statement: tan 90° = 1 cot 90° ? 18. Concept Check One form of a particular reciprocal identity is tan u = two other, equivalent forms of this identity. 1 cot u .