theta=sin^-1 (5/13) ; (x,y)=(-3,1)
how do u find the coordinates of x' and y'??
8 answers
what is (x',y')? (x,y) rotated around (0,0) through the angle theta?
yes
the x' y' is x pime y prime
the x' y' is x pime y prime
ok, so just plug in your numbers:
x' = x cosθ + y sinθ
y' = -x sinθ + y cosθ
If sinθ = 5/13, then cosθ = 12/13
x' = x cosθ + y sinθ
y' = -x sinθ + y cosθ
If sinθ = 5/13, then cosθ = 12/13
i thought the origianl formula is
x = x' cosθ + y' sinθ
y = x' sinθ - y' cosθ
x = x' cosθ + y' sinθ
y = x' sinθ - y' cosθ
It is. But you already have (x,y) and want (x',y')
Your formula gives you (x,y) if you have (x',y'). If you solve it for x,y you will get my formula.
In fact, since (x',y') is (x,y) rotated through θ , that makes (x,y) the image of (x',y') rotated through -θ , which is your formula.
Your formula gives you (x,y) if you have (x',y'). If you solve it for x,y you will get my formula.
In fact, since (x',y') is (x,y) rotated through θ , that makes (x,y) the image of (x',y') rotated through -θ , which is your formula.
okk i have a similar Q.
θ=45degree ; (x,y)=(0, -2)
i got to 0=sqrt2/2 (x'-y')
-2=sqrt2/2 (x'+ y')
then i got stuck....
θ=45degree ; (x,y)=(0, -2)
i got to 0=sqrt2/2 (x'-y')
-2=sqrt2/2 (x'+ y')
then i got stuck....
since sinθ = cosθ = 1/√2,
x' = x/√2 + y/√2 = 1/√2(0-2) = -2/√2 = -√2
y' = -x/√2 + y/√2 = 1/√2 (0-2) = -2/√2 = -√2
so, (x',y') = (-√2,-√2)
Hmmm. It appears that my formula was in error, since clearly we want to end up with (√2,-√2)
So, I must have mixed up my + and - signs. Your formula may be correct after all.
One of us needs to review, and since it's your grade, it might as well be you. :-( Choose points that make it easy to see what your destination must be, and go for it.
x' = x/√2 + y/√2 = 1/√2(0-2) = -2/√2 = -√2
y' = -x/√2 + y/√2 = 1/√2 (0-2) = -2/√2 = -√2
so, (x',y') = (-√2,-√2)
Hmmm. It appears that my formula was in error, since clearly we want to end up with (√2,-√2)
So, I must have mixed up my + and - signs. Your formula may be correct after all.
One of us needs to review, and since it's your grade, it might as well be you. :-( Choose points that make it easy to see what your destination must be, and go for it.
come on help mee~~