Principle of Mathematical Induction

Principle of Mathematical Induction

Question

Find the value of the trigonometric function in the following:

cot open parentheses negative fraction numerator 15 straight pi over denominator 4 end fraction close parentheses










Answer

As tanx and cotx are periodic functions of period straight pi 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.
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#6 {main}</pre>                                (∵ Period is straight pi equals 180 degree)
                     equals space cot open parentheses negative fraction numerator 15 straight pi over denominator 4 end fraction plus fraction numerator 16 straight pi over denominator 4 end fraction close parentheses space equals space cot open parentheses straight pi over 4 close parentheses space equals space 1             (From tables)
Hence,   cot open parentheses negative fraction numerator 15 straight pi over denominator 4 end fraction close parentheses space equals space 1

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