Principle of Mathematical Induction

Principle of Mathematical Induction

Question

Find the value of the trigonometric function in the following:

tan open parentheses fraction numerator 19 straight pi over denominator 3 end fraction close parentheses







Answer

As tanx and cotx are periodic functions of period straight pi space left parenthesis 180 degree right parenthesis.
Therefore, we may add or subtract an integral multiple of straight pi to convert the angle to an acute angle.

tan open parentheses fraction numerator 19 straight pi over denominator 3 end fraction close parentheses space equals space tan open parentheses fraction numerator 19 straight pi over denominator 3 end fraction minus 6 left parenthesis straight pi right parenthesis close parentheses                         (∵ Period is space space space straight pi space equals space 180 degree)
                  equals space tan open parentheses fraction numerator 19 straight pi minus 18 straight pi over denominator 3 end fraction close parentheses space equals space tan open parentheses straight pi over 3 close parentheses space equals space square root of 3                 (From tables)

Hence,  tan open parentheses fraction numerator 19 straight pi over denominator 3 end fraction close parentheses space equals space square root of 3
                 


                     

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