Question

Find the general solution or the general expression for all angles, whose cosine is zero.

Solution

Let $space angle XOP equals straight x$ be any angle.
Now, cos x = 0
$rightwards double arrow$ $OM over OP equals 0$
$rightwards double arrow$ OM = 0
$rightwards double arrow$ OP coincides with OY or OY' which is true when
$straight x equals straight pi over 2 comma space fraction numerator 3 straight pi over denominator 2 end fraction comma space fraction numerator 5 straight pi over denominator 2 end fraction comma space......... space or space straight x space equals space fraction numerator negative straight pi over denominator 2 end fraction comma space fraction numerator negative 3 straight pi over denominator 2 end fraction comma space fraction numerator negative 5 straight pi over denominator 2 end fraction comma space......$
So, general value of x is given by
$straight x equals left parenthesis 2 straight n plus 1 right parenthesis straight pi over 2 comma space space where space straight n element of straight Z$

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Principle Of Mathematical Induction

Find the general solution or the general expression for all angles, whose cosine is zero.

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