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MATH69.204* ANSWERS TO THE FIRST TEST Fall, 1998
- 1. [1 mark] If
, where
f(t) is an even function and g(t) is an odd function, then g(t)
is equal to
- (a)
, (b)
, (c)
, (d)
, (e) 9.
- Answer: (a). It's the only odd function in the sum of the three given functions.
- 2. [1 mark] If f is an odd periodic function of period 4 and if
for all t satisfying
, then f(-135) is equal to - (a) 9, (b) 3, (c) 0,
(d) -3, (e) -9.
- Answer: (e). Because
.
- 3. [1 mark] The circle
in polar coordinates is
- (a)
, (b)
,
(c)
, (d)
,
(e)
.
- Answer: (b). Putting
and
in
, we get
. Cancel r and
rearrange the identity.
- 4. [1 mark] Let
be the equation of a curve in polar
coordinates. Then, using
as a parameter, the parametric equation of
this curve is
- (a)
, (b)
,
, (c)
, \ - (d)
,
, (e)
,
.
- Answer: (e). This follows immediately upon setting
and
.
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Angelo Mingarelli
Mon Oct 5 09:03:18 EDT 1998