Sponsor Area

Principle Of Mathematical Induction

Question

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

Solution

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
$rightwards double arrow$ $WiredFaculty$