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Trigonometric-Functions

In this Trigonometric-Functions you get few formula which are not represented in trigonometric  formula list . You can refer Trigonometric formula by clicking on it . Here few more formula like degrees to radians and vice versa as follows.

Trigonometric-Functions

Relation between Degree and Radian measures:

 180\(^{\circ}\) = \(\prod\) radians.

Using approximate value of \(\prod\) = \(\frac{22}{7}\) we get

 1 radian = \(\frac{180^{\circ}}{\prod}\) =\(57^{\circ}{16}'\) nearly  and also

 \(1^{\circ}\) = \(\frac{\prod}{180}\) radian = 0.01746 radian approximately .

 1' = 60 "

 1\(^{\circ}\) = 60' ( in words 1 degree = 60 minutes)

 1' = \(\frac{1}{60}\) degree

Examples :

1) Convert the following degrees into radian measure.

 a) 30\(^{\circ}\)  b) 45\(^{\circ}\)   c) 60\(^{\circ}\)  d) 75\(^{\circ}\) e) 90\(^{\circ}\) f) 120\(^{\circ}\) g) 135\(^{\circ}\) h)150\(^{\circ}\) i) 180\(^{\circ}\) j) 225\(^{\circ}\) k) 240\(^{\circ}\) l) 270\(^{\circ}\)  m) 315\(^{\circ}\) n) 330\(^{\circ}\) o)360\(^{\circ}\)

Solutions :

 As we know that 1\(^{\circ}\)=\(\frac{\prod}{180}\) radians .

 a) 30\(^{\circ}\) = 30 * \(\frac{\prod}{180}\)

          = \(\frac{\prod}{6}\)

 b) 45 \(^{\circ}\)  =  45 * \(\frac{\prod}{180}\)

           = \(\frac{\prod}{4}\)

c) 60\(^{\circ}\) = 60 * \(\frac{\prod}{180}\)

            = \(\frac{\prod}{3}\)

 d) 75\(^{\circ}\) = 75 * \(\frac{\prod}{180}\)

            = \(\frac{5\prod}{12}\)

 e) 90\(^{\circ}\)  = 90 * \(\frac{\prod}{180}\)

            = \(\frac{\prod}{2}\)

 f) 120\(^{\circ}\) =120 * \(\frac{\prod}{180}\)

            = \(\frac{2\prod}{3}\)

 g) 135\(^{\circ}\) = 135 * \(\frac{\prod}{180}\)

            = \(\frac{3\prod}{4}\)

 h)150\(^{\circ}\) = 150 * \(\frac{\prod}{180}\)

            =\(\frac{5\prod}{6}\)

 i) 180\(^{\circ}\) = 180 * \(\frac{\prod}{180}\)

            = \(\prod\)

 j) 225\(^{\circ}\)  = 225 * \(\frac{\prod}{180}\)

            = \(\frac{5\prod}{4}\)

 k) 240\(^{\circ}\) = 240 * \(\frac{\prod}{180}\)

            = \(\frac{4\prod}{3}\)

 l) 270\(^{\circ}\) = 270 * \(\frac{\prod}{180}\)

            = \(\frac{3\prod}{2}\)

 m) 315\(^{\circ}\) = 315 * \(\frac{\prod}{180}\)

            = \(\frac{7\prod}{4}\)

 n) 330\(^{\circ}\) = 330 * \(\frac{\prod}{180}\)

            = \(\frac{11\prod}{6}\)

 o)360\(^{\circ}\) = 360 * \(\frac{\prod}{180}\)

            = 2\(\prod\)

 2)  Convert the following radians into degree measures .

 a) \(\frac{\prod}{12}\) b) \(\frac{5\prod}{3}\) c) \(\frac{2\prod}{5}\)  d)\(\frac{5\prod}{6}\)

 Solutions :

 As we know that 1 radian = \(\frac{180^{\circ}}{\prod}\)

  a) \(\frac{\prod}{12}\) = \(\frac{180}{12}\)

    = 15\(^{\circ}\)

  b) \(\frac{5\prod}{3}\) = \(\frac{5*180}{3}\)

    = 300\(^{\circ}\)

 c) \(\frac{2\prod}{5}\) = \(\frac{2 *180}{5}\)

    = 72\(^{\circ}\)

d)\(\frac{5\prod}{6}\) = \(\frac{5*180}{6}\)

   =150 \(^{\circ}\)

 3) Convert the following into radian measure .

  a) 40\(^{\circ}\)20'   b) -47\(^{\circ}\)30'

 Solutions :

  a) 40\(^{\circ}\)20'

  1' = \(\frac{1}{60} ^{\circ}\)

  20' = 20 * \(\frac{1}{60} ^{\circ}\)

   = \(\frac{1}{3}\)

  40\(^{\circ}\)20' = 40+ \(\frac{1}{3}\)

     =\(\frac{121}{3}^{\circ}\)

    =\(\frac{121}{3}\)* \(\frac{\prod}{180}\)

    =\(\frac{121\prod}{540}\)radians

 b) -47\(^{\circ}\)30' = -(47 + 30*\(\frac{1}{60} ^{\circ}\))

       = - (47 + 1/2)\(^{\circ}\)

       = - \(\frac{95}{2}^{\circ}\)

      = - \(\frac{95}{2}\)* \(\frac{\prod}{180}\) radians

      = -\(\frac{19\prod}{72}\) radians

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