mat104-bahar_odev3 - C ¸ALIS ¸MA SORULARI-3...

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Unformatted text preview: C ¸ALIS ¸MA SORULARI-3 (2009-2010-Bahar) Dersin Adı: Mat104 Konu: D¨uzlemde Vekt¨orler ve Kutupsal Koordinatlar 1. Kutupsal koordinatları verilen denklemleri sa˘glayan noktaların geometrik yerini ¸ciziniz. (a) 1 ≤ r ≤ 2 ve 0 ≤ θ ≤ π/ 2, (b) r ≤ 0 ve θ = π/ 4. 2. Kartezyen koordinatlarda verilen denklemleri kutupsal koordinatlarda yazınız. (a) xy = 2, (b) ( x + 2) 2 + ( y- 5) 2 = 16, (c) x = 7, (d) x 2 + xy + y 2 = 1. 3. Kutupsal koordinatlarda verilen denklemleri kartezyen koordinatlarda yazınız. (a) r 2 =- 4 r cos θ , (b) r = θ , (c) r = (csc θ )e r cos θ , (d) r = 2cot θ csc θ , (e) r = 5 sin θ- 2cos θ . 4. A¸ sa˘ gıda verilen e˘grileri ¸ciziniz. (a) r = 2cos θ + 1, (b) r = a (1 + sin θ ), (c) r 2 =- sin2 θ , (d) r = 1 + 2sin θ , (e) r = 2cos3 θ . (f) r = cos2 θ (g) r 2 = cos2 θ (h) r = 2 / (1- cos θ ) 5. A¸ sa˘ gıda verilen e˘gri ¸ciftlerinin kesi¸ sim noktalarını bulunuz....
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This note was uploaded on 05/12/2010 for the course MATH 123 taught by Professor Sait during the Spring '09 term at Istanbul Technical University.

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mat104-bahar_odev3 - C ¸ALIS ¸MA SORULARI-3...

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