# converting parametric equations into cartesian form

• Jan 25th 2009, 01:43 PM
sharp357
converting parametric equations into cartesian form
show that x = sin t and y = sin (t + pi/6)

can be written in the form y = ax + b1-x^2 stating the values of a and b

im really stuck
• Jan 25th 2009, 01:49 PM
Jhevon
Quote:

Originally Posted by sharp357
show that x = sin t and y = sin (t + pi/6)

can be written in the form y = ax + b1-x^2 stating the values of a and b

im really stuck

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

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

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

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

can you finish? in particular, pay attention to the $\displaystyle \sin t$'s you see in the above expression. what do you know about $\displaystyle \sin t$ here?
• Jan 25th 2009, 02:19 PM
sharp357
hmmm, i think i can. thanks for the help