PRE-CALCULUS GRADE 12 FORMULA PAGE 
             
                            The following information may be useful when writing this examination. 
             
                              Trigonometry                                            Algebra 
                                  a = rθ                                2                      −b± b2−4ac
                                                                 For ax + bx + c = 0, x =            2a         
            cscθ =    1                   secθ =   1    
                    sinθ                         cosθ
                                                                                    Logarithms 
            cotθ =    1                   tanθ = sinθ  
                    tanθ                         cosθ                    In chemistry, the pH scale measures  
                                                                         the acidity (0…7) or alkalinity (7…14)  
                                          cotθ = cosθ                   of a solution. It is a logarithmic scale  
                                                  sinθ                 in base 10. Thus, a pH of 9 is 10 times  
            sin2θ + cos2θ = 1                                               more alkaline than a pH of 8. 
                                                                       increasing     pH Scale      increasing
            tan2θ +1= sec2θ                                               acidity                   alkalinity
            1+cot2θ = csc2θ                                            01234567891011121314
            sin α +β = sinαcosβ +cosαsinβ 
                ()                                                                  neutral water              
            sin α −β = sinαcosβ −cosαsinβ                                Permutations and Combinations 
                ()
            cos α +β = cosαcosβ−sinαsinβ                                                    n!
                ()                                                                  P =           
                                                                                   n r    n−r !
                                                                                         ()
            cos α −β = cosαcosβ+sinαsinβ 
                ()                                                                             n!
                                                                                C = n =               
                                                                               n r   ()
                                                                                      r    r! n−r !
                            tanα + tanβ                                                      ()
            tan α +β =                     
                ()
                          1−tanα +tanβ                                                                n
                                                                                               ()
                                                                           In the expansion of  a + b   ,  
                           tanα − tanβ                                           the general term is 
            tan α −β =                   
                ()
                          1+tanαtanβ                                                         n−k  k
                                                                                 t   = C a       b  
                                                                                  k+1  n k
            sin2θ = 2sinθcosθ  
            cos2θ = cos2θ −sin2θ
                          2
                   = 2cos θ −1       
                             2
                   =1−2sin θ
            tan2θ =    2tanθ  
                     1−tan2θ
                                                                 
            Pre-Caculus 12 … Formula Page                                                                     Page 1 
                           ROUGH WORK SPACE FOR GRAPHING 
                       (No marks will be given for work done on this page.) 
                                           
       
       
                                                                             
       
       
       
       
                                           
       
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