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Trigonometric Functions

Short Answer Type

581.
Find the general expression for all angles whose sine is zero.

Let $angle XOP space equals space straight x$ be any angle

Draw PM $perpendicular$ X' OX

Then, $space space sinx space equals space MP over OP$

Now, sinx = 0

$rightwards double arrow$ MP = 0

$rightwards double arrow$ OP coincides with OX and OX'

which is true when

$straight x equals 0 comma space straight pi comma space 2 straight pi comma space 3 straight pi comma space........ space Or space minus straight pi comma space minus 2 straight pi comma space minus 3 straight pi comma space...........$

Hence, sinx = 0

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