第1章 1.13

(1)

$r\sin\theta = 1$

$y = r\sin\theta$ から $y = 1$

(2)

$r\cos\theta = -2$

$x = r\cos\theta$ から $x = -2$

(3)

$\theta = \frac{\pi}{3}$

$\theta = \tan^{-1}\dfrac{y}{x}$ $\tan\theta = \dfrac{y}{x}$ から $\tan\dfrac{\pi}{3} = \dfrac{y}{x}$ $\sqrt{3} = \dfrac{y}{x}$ $\therefore y = \sqrt{3}x$

(4)

$r = 3$

$r = \sqrt{x^2 + y^2}$ から $\sqrt{x^2 + y^2} = 3$ $\therefore x^2 + y^2 = 9$

(5)

$r = 2\cos\theta$

$r^2 = 2r\cos\theta$ $r = \sqrt{x^2 + y^2}$ $x = r\cos\theta$ から $\therefore x^2 + y^2 = 2x$

(6)

$r = 4\sin\theta$

$r^2 = 4r\sin\theta$ $r = \sqrt{x^2 + y^2}$ $y = r\sin\theta$ から $\therefore x^2 + y^2 = 4y$