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**Punch** · January 23rd 2010, 06:25 PM

I have solved for part (a) and part (b), including showing OA, problem lies in showing OM... would appreciate some help for showing OM= $2cos\theta+5sin\theta$

**Jhevon** · January 23rd 2010, 07:19 PM

Originally Posted by Punch

I have solved for part (a) and part (b), including showing OA, problem lies in showing OM... would appreciate some help for showing OM= $2cos\theta+5sin\theta$

Using triangle OMA, we have $\sin \theta = \frac {OM}{OA}$ . The result follows easily from there.

also, how did you find OA? seems like you did a lot of work judging from the faint lines i see on the diagram.

**Punch** · January 23rd 2010, 07:34 PM

Thanks!!!

For OA, its far more simple! Draw a line perpendicular to the x-axis from the point (5,2). Let point on perpendicular line on x-axis be X.
So
$OX=5$ .

$tan\theta= \frac{2}{XA}$

$cot\theta=\frac{XA}{2}$

$XA=2cot\theta$

$OA = 5+2cot\theta$

**Jhevon** · January 23rd 2010, 07:48 PM

Originally Posted by Punch

Thanks!!!
For OA, its far more simple! Draw a line perpendicular to the x-axis from the point (5,2). Let point on perpendicular line on x-axis be X.
So
$OX=5$ .

$tan\theta= \frac{2}{XA}$

$cot\theta=\frac{XA}{2}$

$XA=2cot\theta$

$OA = 5+2cot\theta$

ok. i just observed that $AX = OA - 5$ and jumped to $\cot \theta = \frac {OA - 5}2$ right off the bat. not much different from you. good job

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