Find a parameterized curve α(t) whose trace is the circle x^2 + y^2 = 1 such that α(t) runs clockwise around the circle with α(0) = (0,1).
How can I do this problem?
How can I do this problem?
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x=sin(t)
y=cos(t)
α(t) = (sin(t),cos(t))
check
sin^2t+cos^2t=1
α(0) = (sin(0),cos(0)).
= (0,1).
by changing t 0, pi/2, .pi , 3pi/2
we get (0,1). (1,0) (0.-1) (-1.0)
by increasing t α(t) runs clockwise
around the circle
answer α(t) = (sin(t),cos(t))
y=cos(t)
α(t) = (sin(t),cos(t))
check
sin^2t+cos^2t=1
α(0) = (sin(0),cos(0)).
= (0,1).
by changing t 0, pi/2, .pi , 3pi/2
we get (0,1). (1,0) (0.-1) (-1.0)
by increasing t α(t) runs clockwise
around the circle
answer α(t) = (sin(t),cos(t))