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Mathematics
Mathematics
Problem
For the cycloidal curve
x
=
a
(
t
+
sin
t
)
,
y
=
a
(
1
−
cos
t
)
x=a\,(t+\sin t),\;y=a\,(1-\cos t)
x
=
a
(
t
+
sin
t
)
,
y
=
a
(
1
−
cos
t
)
, obtain the equation of the tangent at
t
=
π
2
t=\dfrac{\pi}{2}
t
=
2
π
in a form that does not contain the parameter
t
t
t
. a)
x
+
y
−
a
π
2
=
0
x+y-\dfrac{a\pi}{2}=0
x
+
y
−
2
aπ
=
0
b)
x
−
y
−
a
π
2
=
0
x-y-\dfrac{a\pi}{2}=0
x
−
y
−
2
aπ
=
0
c)
x
−
y
+
a
π
2
=
0
x-y+\dfrac{a\pi}{2}=0
x
−
y
+
2
aπ
=
0
d)
x
−
y
−
a
=
0
x-y-a=0
x
−
y
−
a
=
0
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