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FP3 problem (parametric equations) watch

1. x=t+sint
y=1-cost

a) Show that √(x²+y²)=2cos½t

I've gotten to
RHS=2cost½t
=2√(cos2t/2 + 1/2)

LHS=√(t²+2tsint-2cost+1)

But I'm not sure what to do after that
2. (Original post by bobbricks)
x=t+sint
y=1-cost

a) Show that √(x²+y²)=2cos½t
Perhaps I'm missing something but

and

so something doesn't look right here.
3. (Original post by atsruser)
Perhaps I'm missing something but

and

so something doesn't look right here.
I imagine its asking you to show it works for all values of t, and so you want to sub your x and y into the LHS and show it = RHS.
4. (Original post by SamKeene)
I imagine its asking you to show it works for all values of t, and so you want to sub your x and y into the LHS and show it = RHS.
How do you show LHS=RHS for all values of t (without using specific values of x and y)?
5. (Original post by bobbricks)
x=t+sint
y=1-cost

a) Show that √(x²+y²)=2cos½t

I've gotten to
RHS=2cost½t
=2√(cos2t/2 + 1/2)

LHS=√(t²+2tsint-2cost+1)

But I'm not sure what to do after that
I got

√(x²+y²)=t +sin½t

i used sint = 2sin(t)/2cos(t/2)
and cost = 1 - 2sin2(t/2) which leads to a perfect square

is this any good?

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