online user counteronline user counter

MATHMAA

Only Search Your Site

math-formula-sheet-doubleangles

Probability Introduction :

In this "math-formula-sheet-doubleangles"  , double and triple angles of trigonometric ratios and their derived formula you can see.

I. Double Angles

 1) Sin(\(2\Theta\) )= 2 Sin\(\Theta\)Cos\(\Theta\)

  2) Cos(\(2\Theta\))= \(Cos^{2}\Theta - Sin^{2}\Theta\)

                            = \(2Cos^{2}\Theta - 1\)

                            = \(1-2Sin^{2}\Theta\)

  a)\(Cos^{2}( \Theta ) =\frac{1+Cos(2\Theta)}{2}\)

  b)\(Cos( \Theta ) =\sqrt{\frac{1+Cos(2\Theta)}{2}}\)

  c)\(Sin^{2}( \Theta ) =\frac{1-Cos(2\Theta)}{2}\)

  d)\(Sin( \Theta ) =\sqrt{\frac{1-Cos(2\Theta)}{2}}\)

 3) Tan\((2\Theta) =\frac{2Tan\Theta}{1-Tan^{2}\Theta}\)

 4) Sin\((2\theta) = \frac{2Tan\Theta}{1+Tan^{2}\Theta}\)

 5) Cos\((2\Theta)=\frac{1-Tan^{2}\Theta}{1+Tan^{2}\Theta}\)

II. Their derived formula(half angles)

  Replace \(2\Theta\) by \(\Theta\) and \(\Theta\) by \(\frac{\Theta}{2}\) in above formula, we get

 1)Sin\((\Theta)=2Sin\frac{\Theta}{2}Cos\frac{\Theta}{2}\)

  2)Cos\((\Theta) = Cos^{2}(\frac{\Theta}{2}) - Sin^{2}(\frac{\Theta}{2})\)

           =\(2Cos^{2}(\frac{\Theta}{2})-1\)

           =1-\(2Sin^{2}(\frac{\Theta}{2})\)

 3)Tan\((\Theta)=\frac{2Tan(\frac{\Theta}{2})}{1-Tan^{2}(\frac{\Theta}{2})}\)

 4) \(Tan^{2}(\Theta)=\frac{1-Cos(2\Theta)}{1+Cos(2\Theta)}\)

 5)\(Tan(\Theta)=\sqrt{\frac{1-Cos(2\Theta)}{1+Cos(2\Theta)}}\)

III Triple angles of Trigonometric ratios Sin, Cos and Tan as follows:

 1) Sin(3\(\Theta)= 3Sin(\Theta)- 4 Sin^{3}(\Theta)\)

    a) \(Sin^{3}(\Theta) =\frac{3Sin(\Theta)-Sin(3\Theta)}{4}\)

 2) Cos(3\(\Theta)= 4 Cos^{3}(\Theta)- 3 Cos(\Theta)\)

     a)\(Cos^{3}(\Theta) =\frac{3Cos(\Theta)+Cos(3\Theta)}{4}\)

  

  3) Tan(3\(\Theta)= \frac{3Tan(\Theta)-Tan^{3}(\Theta)}{1-3Tan^{2}(\Theta)}\)



     

 

  <<BACK

<<MATH FORMULA SHEET                              SIN COS SUM DIFFERENCE FORMULA


SHARE YOU ENORMOUS EFFORT AND SMART EXAMPLES HERE

!! NEED MORE HELP !!

SBI! Case Studies