FORMULAS FROM GEOMETRY AND TRIGONOMETRY GEOMETRY

Let r or R denote radius, h altitude, b length of base, B  area of base, s slant height, and  central angle in radian measure.

1. Circle: circumference = , area =
2. Circular arc: length =
3. Circular sector: area =
4. Circular segment: area =
5. Triangle: area =
6. Trapezoid: area =
7. Sphere: volume = , area of surface =
8. Right circular cylinder: volume = , lateral surface area =
9. Right circular cone: volume = , lateral surface area =
10. Frustum of cone: volume = , lateral surface area =
11. Prism: volume =
12. Pyramid: volume =

 

TRIGONOMETRY

Law of Cosines.
              If A, B, and C are the interior angles of a triangle and a, b, and c are the sides respectively opposite to these angles, then




 

Pythagorean Identities.




 

Reduction Formulas.


              
               
                     

Addition Formulas.




Double-Angle Formulas.




Half-Angle Formulas.


                           

Sums and Products.




 

A SHORT TABLE OF INTEGRALS

Some Fundamental Forms

1.
2.
3.
4.
5.                            ()
6.

Rational Forms Involving

7.
8.
9.
10.
11.
12.
13.

Forms Involving 

14.
15.
16.
17.
18a.                    ( a > 0 )
18b.                     ( a < 0 )
19.
20.
21.

Forms Involving   and 

22.                                                 if  a > 0             
23.                       if 
24.                    if 

Forms involving 

25.                                                    if  , a > 0
26.
27.
28.
29.
30.
31.
32.
33.
34.

Forms Involving 

35.
36.
37.

38.

39.
                             

40.



41.
42.
43.
                             
44.

Forms Involving 


45.
46.
                      
47.
                             
48.
                            
49.
                             

50.
                   
51.
52.
53.
                             
54.

Forms Involving 

55.
56.
57.
58.
59.
60.
61.
62.
63.

Trigonometric Forms


64.
65.
66.
67.
68.
69.
70.
71.
72.
73.
74.
75.
76.
77.
78.
79.
80.
81.
82.
83.
84.
85a.
85b.
86a.                              if 
86b.                         if 
87a.                                     if 
87b.                         if 

Inverse Trigonometric Forms


88.
89.
90.

Exponential and Logarithmic Forms

91.
92.
93.
94.
95.
96.
97.
98.
99.
100.

Hyperbolic Forms

101.
102.
103.
104.
105.
106.
107.
108.
109.
110.
111.
112.
113.
114.
115.
116.

Wallis’s Formulas


117.
                                                   if n is an odd integer > 1;
                                               if n is a positive even integer.
118.
              if n is an odd integer > 1;
                  if m is an odd integer > 1;
                 if m and n are both positive even integers.