Page:Elements of the Differential and Integral Calculus - Granville - Revised.djvu/26

16. Volume of prism$\scriptstyle {=Ba}$.

17. Volume of pyramid$\scriptstyle {={\frac {1}{3}}Ba}$.

18. Volume of right circular cylinder$\scriptstyle {=\pi r^{2}a}$.

19. Lateral surface of right circular cylinder$\scriptstyle {=2\pi ra}$.

20. Total surface of right circular cylinder$\scriptstyle {=2\pi r(r+a)}$.

21. Volume of right circular cone$\scriptstyle {={\frac {1}{3}}\pi r^{3}a}$.

22. Lateral surface of right circular cone$\scriptstyle {=\pi rs}$.

23. Total surface of right circular cone$\scriptstyle {=\pi r(r+s)}$.

24. Volume of sphere$\scriptstyle {={\frac {4}{3}}\pi r^{3}}$.

25. Surface of sphere$\scriptstyle {=4\pi r^{2}}$.

26. $\scriptstyle {\sin x={\frac {1}{\csc x}};\ \cos x={\frac {1}{\sec x}};\ \tan x={\frac {1}{\cot x}}}$.

27. $\scriptstyle {\tan x={\frac {\sin x}{\cos x}};\ \cot x={\frac {\cos x}{\sin x}}}$.

28. $\scriptstyle {\sin ^{2}x+\cos ^{2}x=1;\ 1+\tan ^{2}x=\sec ^{2}x;\ 1+\cot ^{2}x=\csc ^{2}x}$.

29. ${\begin{array}{l}\scriptstyle {\sin x=\cos \left({\frac {\pi }{2}}-x\right);}\\\scriptstyle {\cos x=\sin \left({\frac {\pi }{2}}-x\right);}\\\scriptstyle {\tan x=\cot \left({\frac {\pi }{2}}-x\right).}\end{array}}$

30. ${\begin{array}{l}\scriptstyle {\sin(\pi -x)=\sin x;}\\\scriptstyle {\cos(\pi -x)=-\cos x;}\\\scriptstyle {\tan(\pi -x)=-\tan(x).}\end{array}}$

31. $\scriptstyle {\sin(x+y)=\sin x\cos y+\cos x\sin y}$.

32. $\scriptstyle {\sin(x-y)=\sin x\cos y-\cos x\sin y}$.

33. $\scriptstyle {\cos(x\pm y)=\cos x\cos y\mp \sin x\sin y}$.

34. $\scriptstyle {\tan(x+y)={\frac {\tan x+\tan y}{1-\tan x\tan y}}}$.

35. $\scriptstyle {\tan(x-y)={\frac {\tan x-\tan y}{1+\tan x\tan y}}}$.

36. $\scriptstyle {\sin 2x=2\sin x\cos x;\ \cos 2x=\cos ^{2}x=\sin ^{2}x;\ \tan 2x={\frac {2\tan x}{1-\tan ^{2}x}}}$.

37. $\scriptstyle {\sin x=2\sin {\frac {x}{2}}\cos {\frac {x}{2}};\ \cos x=\cos ^{2}{\frac {x}{2}}-\sin ^{2}{\frac {x}{2}};\ \tan x={\frac {2\tan {\frac {1}{2}}x}{1-\tan ^{2}{\frac {1}{2}}x}}}$.

38. $\scriptstyle {\cos ^{2}x={\frac {1}{2}}+{\frac {1}{2}}\cos 2x;\ \sin ^{2}x={\frac {1}{2}}-{\frac {1}{2}}\cos 2x}$.

39. $\scriptstyle {1+\cos x=2\cos ^{2}{\frac {x}{2}};\ 1-\cos x=2\sin ^{2}{\frac {x}{2}}}$.

40. $\scriptstyle {\sin {\frac {x}{2}}=\pm {\sqrt {\frac {1-\cos x}{2}}};\ \cos {\frac {x}{2}}=\pm {\sqrt {\frac {1+\cos x}{2}}};\ \tan {\frac {x}{2}}=\pm {\sqrt {\frac {1-\cos x}{1+\cos x}}}}$.

41. $\scriptstyle {\sin x+\sin y=2\sin {\frac {1}{2}}(x+y)\cos {\frac {1}{2}}(x-y)}$.

42. $\scriptstyle {\sin x-\sin y=2\cos {\frac {1}{2}}(x+y)\sin {\frac {1}{2}}(x-y)}$.

43. $\scriptstyle {\cos x+\cos y=2\cos {\frac {1}{2}}(x+y)\cos {\frac {1}{2}}(x-y)}$.

44. $\scriptstyle {\cos x-\cos y=-2\sin {\frac {1}{2}}(x+y)\sin {\frac {1}{2}}(x-y)}$.

45. $\scriptstyle {{\frac {a}{\sin A}}={\frac {b}{\sin B}}={\frac {c}{\sin C}};}$ Law of Sines.

46. $\scriptstyle {a^{2}=b^{2}+c^{2}-2bc\cos A;}$ Law of Cosines.

47. $\scriptstyle {d={\sqrt {(x_{1}-x_{2})^{2}+(y_{1}-y_{2})^{2}}};}$ distance between points $\scriptstyle {(x_{1},y_{1})}$ and $\scriptstyle {(x_{2},y_{2})}$.

48. $\scriptstyle {d={\frac {Ax_{1}+By_{1}+C}{\pm {\sqrt {A^{2}+B^{2}}}}};}$ distance from line $\scriptstyle {Ax+By+C=0}$ to $\scriptstyle {(x_{1},y_{1})}$.