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Principle Of Mathematical Induction

Question

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Find the value of the trigonometric function in the following:

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

Solution

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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Some More Questions From Principle of Mathematical Induction Chapter

If in two circles, arcs of the same length subtend angles 60° and 75° at the centre, find the ratio of their radii.

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