Math 215 Precalculus Review Notes
                Formulas
                                     2
                area of circle: A = πr
                circumference of a circle: C =2πr
                volume of a sphere: V = 1   3
                                        3πr
                                                          2
                surface of a right circular cylinder: S =2πr +2πrh
                                                         2h
                volume of a right circular cylinder: V = πr
                Pythagorean Theorem: In a right triangle with hypotenuse length c and legs with lengths b and a,
                then a2 +b2 = c2.
                                          Properties of the Exponential Function
                       0         1
                   1. b =1andb =b
                       x y   x+y
                   2. b b = b
                       x y    xy
                   3. (b ) = b
                       −x    1
                   4. b   = x
                            b
                       x
                      b     x−y
                   5.  y =b
                      b
                                                Properties of the Logarithm
                The logarithm is the inverse of the exponential function. Thus,
                                log  x                                               logb x
                                    (b )=log(exp x)=x         and     exp (log x)=b       =x.
                                   b         b    b                      b    b
                Special cases,
                                    log            1                                0
                                        (b)=log(b)=1         and     log (1) = log (b )=0.
                                       b        b                       b        b
                   1. Property 1: log PQ=log P+log Q
                                    b         b        b
                   2. Property 2: log Pn = nlog P
                                    b           b
                   3. Property 3: log P =log P−log Q
                                    b Q      b       b
                   4. Property 4: (Change of Base Formula)     log x = logbx
                                                                  a     log a
                                                                           b
                                                               1
                                                       Trigonometry
                Definitions
                   1. sinθ =  opposite
                            hypotenuse
                   2. cosθ =  adjacent
                             hypotenuse
                   3. tanθ = opposite
                             adjacent
                   4. cscθ =  1
                            sinθ
                   5. secθ =  1
                            cosθ
                   6. cotθ =  1
                             tanθ
                Identities
                        2       2
                   1. sin θ +cos θ=1
                        2           2
                   2. tan θ+1=sec θ
                            2       2
                   3. 1+cot θ =csc θ
                   4. cos(−θ)=cosθ
                   5. sin(−θ)=−sinθ
                   6. cos(θ − π)=sinθ
                             2
                   7. sin(θ − π)=−cosθ
                             2
                   8. sin(α +β)=sinαcosβ +sinβcosα
                   9. cos(α+β)=cosαcosβ−sinαsinβ
                 10. tan(α+β)= tanα+tanβ
                                  1−tanαtanβ
                 11. sin(α −β)=sinαcosβ −sinβcosα
                 12. cos(α−β)=cosαcosβ+sinαsinβ
                 13. tan(α−β)= tanα−tanβ
                                  1+tanαtanβ
                 14. sin(2θ)=2sinθcosθ
                                  2      2
                 15. cos(2θ)=cos θ−sin θ
                 16. tan(2θ)= 2tanθ
                                      2
                               1−tan θ
                              r
                 17. cos(θ)=    1+cosθ
                         2          2
                              r
                 18. sin(θ)=    1−cosθ
                         2          2
                                                              2