converting parametric equations into cartesian form

**sharp357** · January 25th 2009, 01:43 PM

show that x = sin t and y = sin (t + pi/6)

can be written in the form y = ax + b√1-x^2 stating the values of a and b

im really stuck

**Jhevon** · January 25th 2009, 01:49 PM

Originally Posted by sharp357

show that x = sin t and y = sin (t + pi/6)

can be written in the form y = ax + b√1-x^2 stating the values of a and b

im really stuck

$y = \sin \left( t + \frac {\pi}6 \right)$

$= \sin t \cos \frac {\pi}6 + \sin \frac {\pi}6 \cos t$ ........by the addition formula for sine

$= \frac {\sqrt{3}}2 \sin t + \frac 12 \cos t$

$= \frac {\sqrt{3}}2 \sin t + \frac 12 \sqrt{ 1 - \sin^2 t }$

can you finish? in particular, pay attention to the $\sin t$ 's you see in the above expression. what do you know about $\sin t$ here?

**sharp357** · January 25th 2009, 02:19 PM

hmmm, i think i can. thanks for the help

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