30. A pair of parametric equations is given. Find a rectangular-coordinate equation for the curve by eliminating the parameter. Sketch the graph. п (а) х — sec t y = tan?t 0

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ISBN:9780470458365
Author:Erwin Kreyszig
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Part G

30. A pair of parametric equations is given. Find a rectangular-coordinate equation for the curve by
eliminating the parameter. Sketch the graph.
п
(а) х — sec t
y = tan?t 0 <t <
2
(b) х — сost
= cos(2t)
= t?
y = t – 2 te [2, 4]
х 3 3 cos t
y = 3 sin t t E [0, "]
x = 3 sin t y = 3 cos t 0<t<
16 sin (t) y = 3 cos(t) te [0, 7]
y = 16 cos? t
(f) x =
(g) x =
4 sin t
<t
2
Transcribed Image Text:30. A pair of parametric equations is given. Find a rectangular-coordinate equation for the curve by eliminating the parameter. Sketch the graph. п (а) х — sec t y = tan?t 0 <t < 2 (b) х — сost = cos(2t) = t? y = t – 2 te [2, 4] х 3 3 cos t y = 3 sin t t E [0, "] x = 3 sin t y = 3 cos t 0<t< 16 sin (t) y = 3 cos(t) te [0, 7] y = 16 cos? t (f) x = (g) x = 4 sin t <t 2
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