1. ## Showing(2)

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

2. 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=$\displaystyle 2cos\theta+5sin\theta$
Using triangle OMA, we have $\displaystyle \sin \theta = \frac {OM}{OA}$. 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.

3. 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
$\displaystyle OX=5$.

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

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

$\displaystyle XA=2cot\theta$

$\displaystyle OA = 5+2cot\theta$

4. 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
$\displaystyle OX=5$.

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

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

$\displaystyle XA=2cot\theta$

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