Principle of Mathematical Induction

Principle of Mathematical Induction

Question

Find the values of the trigonometric functions in the following:

cosec left parenthesis negative 1410 degree right parenthesis



Answer

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∴  We may add or subtract an integral multiple of 2 straight pi space or space 360 degree to convert the angle to an acute angle. Also, 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.
cosec left parenthesis negative 1410 degree right parenthesis space equals space cosec left square bracket left parenthesis negative 1410 degree plus 4 left parenthesis 360 degree right parenthesis right square bracket                    [∵  Period is 2 straight pi space equals space 360 degree]
                         space space space space equals space cosec space left parenthesis negative 1410 degree plus 1440 degree right parenthesis space equals space cosec 30 degree space equals space fraction numerator 1 over denominator sin 30 degree end fraction space equals space fraction numerator 1 over denominator 1 divided by 2 end fraction space equals space 2
Hence,  cosec left parenthesis negative 1410 degree right parenthesis space equals space 2


                     

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