常用函数曲线图形

Figure 5:
8a3 Figure 6: y= 2 x + 4a2 x = 2a tan θ
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Figure 7: Dept. of Math.
ve
ÒãÔ
r = a cos 3θ 2
XeL aTe
Æ
√ x+ √ y= √ a
ù
¯
ù
y = 2a cos2 θ
NorthWest University
Figure 20:
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Figure 21:
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Dept. of Math.
ve
±
7
Figure 22: x = 1 a(3 cos φ − cos 3φ) 2 y = 1 a(3 sin φ − sin 3φ) 2
XeL aTe
y = a(1 − cos t) r = a sin θ cos2 θ
NorthWest University
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Figure 2:
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Figure 3:
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Figure 4: Dept. of Math.
XeL aTe
Figure 1:
ø
»
Î
rθ = a
â
r = aθ(
Õ
)
r = aeθ (
Õ
Æ
)
´»
1
x3 + y 3 = a3
2
2
2
NorthWest University x = a cos3 t y = a sin3 t
XeL aTe
ÒHale Waihona Puke Baidu«Ë ùy
2
= x2
a−x a+x
21:28 December 6, 2011
ù(x
2
+ y 2 )2 = ax2 y
Æ»
(a2 + x2 )y = abx
NorthWest University
Figure 23: x = 2a cos ϕ + a cos 2ϕ y = 2a sin ϕ − a sin 2ϕ
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Figure 24: Dept. of Math. r = a cos 2θ sec θ 8
Figure 8:
Figure 9:
120
ve
1 180 0 0; 0 210
150
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240
Figure 10:
Dept. of Math.
XeL aTe
ÒãÔ
r = a sin 3θ
ÓãÔ
90 2
r = a cos 2θ
60
30
360 2
1
330
300 270
ÓãÔ
r = a sin 2θ
3
ve
«
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Figure 19: Dept. of Math.
XeL aTe
ã
y 2 (2a − x) = x3 , ( x = 2a) Figure 18: x = a(cos t + t sin t) y = a(sin t − t cos t)
Ñ
ß (Õ
6
)
NorthWest University x = a(t − sin t)
NorthWest University
Figure 11: a(1 + cos θ)
±
r = a(1 − cos θ)
Figure 12:
Î
ve
Î
r 2 = a2 sin 2θ Figure 14:
Figure 13:
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Dept. of Math.
XeL aTe
ùx
2
+ y 2 + ax = a x2 + y 2
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Figure 16:
℄
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Dept. of Math. 5
XeL aTe
´ ã» (x + y ) = 3axy Ǒ x + y + a = 0, Ô
3 3
a=4/3
y = a cosh
x a
(e ùy = a 2
x a
+ e− a )
x
NorthWest University
Figure 17:
±
r =
r 2 = a2 cos 2θ
ù(x
2
+ y 2 )2 = a2 (x2 − y 2 )
ù(x
2
+ y 2 )2 = 2a2 xy
Î
y = e−x
2
4
NorthWest University
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Figure 15: 3at x= 1 + t3 2 y = 3at = tx 1 + t3