SOLUTION: <pre><b>Find the exact values for the trig functions, with the radian measure: 15<font face = "symbol">p</font>/4</pre>

Algebra ->  Trigonometry-basics -> SOLUTION: <pre><b>Find the exact values for the trig functions, with the radian measure: 15<font face = "symbol">p</font>/4</pre>      Log On


   

Question 35485: 
Find the exact values for the trig functions, with the radian measure:
                          15p/4
Found 2 solutions by venugopalramana, AnlytcPhil:
Answer by venugopalramana(3286) About Me  (Show Source):
You can put this solution on YOUR website!
ANGLE =15*PI/4=16*PI/4-PI/4=-PI/4....THAT IS WE TAKE TRIANGLE WITH ANGLE PI/4 AND APPLY THE RULE OF SIGNS..."ALL SILVER TEA CUPS"...THAT IS IT IS AN ISOCELLES RIGHT ANGLED TRIANGLE.HENCE LET BOTH SIDES BE 1 EACH. THEN HYPOTENUSE =SQRT(1^2+1^2)=SQRT(2)
SO
SIN (PI/4)=1/SQRT(2)=SQRT(2)/2=1.4142/2=0.7071
COSEC(PI/4)=SQRT(2)=1.4142
COS(PI/4)= 1/SQRT(2)=SQRT(2)/2=1.4142/2=0.7071
SEC(PI/4)=SQRT(2)=1.4142
TAN(PI/4)=1/1=1
COT(PI/4)=1/1=1
HENCE
SIN (-PI/4)=-1/SQRT(2)=-SQRT(2)/2=-1.4142/2=-0.7071
COSEC(-PI/4)=-SQRT(2)=-1.4142
COS(-PI/4)= 1/SQRT(2)=SQRT(2)/2=1.4142/2=0.7071
SEC(-PI/4)=SQRT(2)=1.4142
TAN(-PI/4)=-1/1=-1
COT(-PI/4)=-1/1=-1

Answer by AnlytcPhil(1806) About Me  (Show Source):
You can put this solution on YOUR website!

Find the exact values for the trig functions, with the radian measure:
                          15p/4

------------------------------------------------------

                         sin(15p/4) = 

                   sin(16p/4 - p/4) =

                      sin(4p - p/4) =
    
sin(4p)·cos(p/4) - cos(4p)·sin(p/4) =

          0·cos(p/4) - (1)·sin(p/4) =

                          -sin(p/4) = 
                              _ 
                            -Φ2/2

------------------------------------------------------

                         cos(15p/4) = 

                   cos(16p/4 - p/4) =

                      cos(4p - p/4) =
    
cos(4p)·cos(p/4) - sin(4p)·sin(p/4) =

          1·cos(p/4) - (0)·sin(p/4) =

                           cos(p/4) = 
                              _ 
                             Φ2/2

------------------------------------------------------


                         tan(15p/4) = 

                  sin(p/4)/cos(p/4) =
     
                              _ 
                             Φ2/2 
                            ————— =
                            -Φ2/2
 
                                -1
    
------------------------------------------------------

                         sec(15p/4) =

                             1
                       ———————————— =
                        cos(15p/4) 

                               1
                             —————— =
                              Φ2/2

                                2
                             —————— =
                               Φ2
                                 _
                          2     Φ2
                        ———— · ————— =
                         Φ2     Φ2                        
                                 _
                               2Φ2  
                              ————— =
                                2

                               1 _
                               2Φ2  
                              ————— =
                                2
                                1
                                  _
                                 Φ2

------------------------------------------------------


                         csc(15p/4) =

                             1
                       ———————————— =
                        sin(15p/4) 

                               1
                             —————— =
                             -Φ2/2

                                2
                           - —————— =
                               Φ2
                                 _
                          2     Φ2
                      - ———— · ————— =
                         Φ2     Φ2                        
                                 _
                               2Φ2  
                            - ————— =
                                2

                               1 _
                               2V2  
                            - ————— =
                                2
                                1

                               _
                             -Φ2

------------------------------------------------------

                         cot(15p/4) =

                             1
                       ———————————— =
                        tan(15p/4)

                            1/(-1)  =

                                -1  

Edwin McCravy
AnlytcPhil@aol.com