Principle of Mathematical Induction

Principle of Mathematical Induction

Question

Find the values of other five trigonometric functions of the following:

sinx space equals space 3 over 5 comma space straight x lies in second quadrant

Answer

Here, sinx = 3 over 5
sinx>0, cosx<0, tanx<0, cosecx>0, secx<0, cotx<0       (∵ x lies in quadrant II)
Now,         sin squared straight x plus cos squared straight x space equals space 1 space space space space rightwards double arrow space space space space space space 9 over 25 plus cos squared straight x space equals space 1 space space space rightwards double arrow space space space space cos squared straight x space equals space 16 over 25 space space space space rightwards double arrow space space space cosx space equals space plus-or-minus 4 over 5

rightwards double arrow                        cosx space equals space minus 4 over 5                                              (∵ cosx is -ve)
                         cosecx space equals space 1 over sinx space equals space 5 over 3 comma space      secx space equals space 1 over cosx space equals space minus 5 over 4
                          tanx space equals space sinx over cosx space equals space minus 3 over 4 comma      cotx space equals space cosx over sinx space equals space minus 4 over 3

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