AP Calculus BC Quiz
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PARAMETRIC, POLAR, AND VECTOR FUNCTIONS
Question 1
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For
x
(
t
)
=
sin
t
+
sin
2
t
x(t)=\sin t+\sin 2t
x
(
t
)
=
sin
t
+
sin
2
t
and
y
(
t
)
=
cos
t
+
cos
2
t
y(t)=\cos t+\cos 2t
y
(
t
)
=
cos
t
+
cos
2
t
, find
d
y
d
x
\frac{dy}{dx}
d
x
d
y
in terms of
t
t
t
.
A
−
sin
t
−
2
sin
2
t
cos
t
+
2
cos
2
t
\dfrac{-\sin t-2\sin 2t}{\cos t+2\cos 2t}
cos
t
+
2
cos
2
t
−
sin
t
−
2
sin
2
t
B
cos
t
+
2
cos
2
t
−
sin
t
−
2
sin
2
t
\dfrac{\cos t+2\cos 2t}{-\sin t-2\sin 2t}
−
sin
t
−
2
sin
2
t
cos
t
+
2
cos
2
t
C
cos
t
+
cos
2
t
cos
t
+
2
cos
2
t
\dfrac{\cos t+\cos 2t}{\cos t+2\cos 2t}
cos
t
+
2
cos
2
t
cos
t
+
cos
2
t
D
(
−
sin
t
−
2
sin
2
t
)
(
cos
t
+
2
cos
2
t
)
(-\sin t-2\sin 2t)(\cos t+2\cos 2t)
(
−
sin
t
−
2
sin
2
t
)
(
cos
t
+
2
cos
2
t
)
E
−
sin
t
−
2
sin
2
t
sin
t
+
sin
2
t
\dfrac{-\sin t-2\sin 2t}{\sin t+\sin 2t}
sin
t
+
sin
2
t
−
sin
t
−
2
sin
2
t
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