To convert parametric to Cartesian systems, you need to find a way to get rid of the t's.
In this case, the t's are inside trigonometric functions, so we're going to use a very famous trig identity you should memorize:
If we plug sin(t) and cos(t) into that equation only x and y variables will be left!
BUT there's one thing. The given cos(t + pi/6) has nasty extra stuff in it. However, part a gives you a tip on how to relate x and y to a nice clean cos(t)
So if we do a little rearranging:
Now we can plug these into the famous trig identity!
Do a little bit of adjustments to get that final form asked for, and you'll be able to find those integers of a and b. ;)
In this case, the t's are inside trigonometric functions, so we're going to use a very famous trig identity you should memorize:
If we plug sin(t) and cos(t) into that equation only x and y variables will be left!
BUT there's one thing. The given cos(t + pi/6) has nasty extra stuff in it. However, part a gives you a tip on how to relate x and y to a nice clean cos(t)
So if we do a little rearranging:
Now we can plug these into the famous trig identity!
Do a little bit of adjustments to get that final form asked for, and you'll be able to find those integers of a and b. ;)