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albear · Jun 17, 2007, 08:46 AM

x=t-2sint, y=1-2cost

show that the curve crosses the x axis where t=pi/3 and t=5pi/3

I understand that you have to solve y=0 but alli can get is t=pi/3

Capuchin · Jun 17, 2007, 08:51 AM

can't you just put both t's into the equation for y and show that y = 0 and therefor it's crossing the x axis?

galactus · Jun 17, 2007, 08:52 AM

Always graph if at all possible.

albear · Jun 17, 2007, 08:56 AM

I could but I don't have access to a graph creator and no be cause that would be the wrong way of answering that qn and I wouldn't get marks, I have to solve y=0 which makes cost=1/2 which makes t=pi/3 but I cannot find out how to make it also equal 5pi/3

galactus · Jun 17, 2007, 08:58 AM

$2{\pi}-\frac{\pi}{3}=\frac{5{\pi}}{3}$

I'd say get familiar with the unit circle. This is the properties of the trig functions you should know.

$0=1-2cos(t)$

$cos(t)=\frac{1}{2}$

$t=\frac{(6C+1){\pi}}{3} \;\ or \;\ \frac{(6C-1){\pi}}{3}$

If C=0, then $t=\pm\frac{\pi}{3}$

If C=1, then $t=\frac{7\pi}{3} \;\ or \;\ \frac{5\pi}{3}$

If C=2, then $t=\frac{13\pi}{3} \;\ or \;\ \frac{11\pi}{3}$

and so on...

Though, anything that exceeds 2Pi you probably can disregard.

albear · Jun 17, 2007, 09:06 AM

Thank you, guess I need to read up on my C3 then