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数学 高校生

なぜ、(2)と(3)は、極2分のπを通ると記述しなくてはいけないんですか?お願いします!

極方程式 ○dO00。 OOOO0 110 基本例題 67 直交座標の方程式 次の直交座標に関する方程式を,極方程式で表せ。 (1) x-V3y-2=0 (3) y=4x (2) x°+y°=-2x D.105 基本事項 CHART lOLUTION MOITUIO 直交座標の方程式 一 極方程式 =rcos0, y=rsin0, x'+y°=r x, yをr, 0を用いて表す。 また, 得られた極方程式が三角関数の加法定理など を用いることで,より簡単な方程式になるときは, そのように変形する。 (1)では途中で, r(acosθ+bsin0)=c の形の極方程式が得られる。このとき, 三角関数の合成を用いても簡単な形になるが, 加法定理 cos(α-B)=cos acosβ+sinasinβ を利用すると, rcos(0-α)=d の形とな り,表す図形がわかりやすい。 (2),(3)では r=0 が極を表すことに注意し, 他方に含まれていることを確認す 日A04 る。 解答 (1) x-V3y-2=0 に x=rcosθ, y=rsin0 を代入すると 合 rcos 0-/3rsin0-2 r(cos0-V3sin0)=2 0+A0rA Cosa G6D =0 /3 ゆえにcoso+sine-(-)-15grs よって、求める極方程式は(rcos(0-2)=1 2' 5 -π=1 3 rcos 0 3 2 (2) x°+y°=-2x に x°+y°=ア, x3rcos0 を代入すると r(r+2cos0)=0 r=0 または r=-2cos0 利用 合=-2rcos 0 ゆえに 甘る A代職 Tπ を通る。 J 極0の極座標は中 ア=0 は極を表し,r=-2cos 0 は極(0, 2 よって, 求める極方程式は 口(3) y=4x に x=rcos0, y=rsin0 を代入すると (0, 0) 0は任意の数。 r=-2cos0 r(rsin'0-4cos0)=0 DB(- *パ'sin'0=4rcos@ ゆえに r=0 または rsin'0=4cos 0 r=0 は極を表し, rsin'0=4cosθ は極(0, (π を通る。 2 よって, 求める極方程式は rsin'0=4cos 0 PRACTICE…67° 次の直交座標に関する方程式を, 極方程式で表せ。 (1) x+y+2=0 面 (2) (x°+y?-4y=0 来(3) x-y°=-

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英語 高校生

英文2段落目3文目のfor fairy talesのforは使ってという意味で使われているんでしょうか。、? また、第4段落5文目が上手く訳せません、、、 これは過去完了でしょうか??それとも、彼女は持っていた、1番初めのwrittenとdrawnをみたいにただの過去形で... 続きを読む

Your group is preparing a poster presentation entitled "The Woman Who 第5問(配点 15) c 15e uW y bos AS neighb A (20d dos Tot nongo in b s saoodt time a Wanti Created Peter Rabbit "using information from the magazine article below nob land her e Ved Pig ト popular character, Peter Rabbit. She brought her characters to life in b witty stories with finely detailed watercolors. a Br herit The daughter of wealthy parents, Helen Beatrix Potter was born on July 28, 1866 in South Kensington, London. She was educated at home and developed a love of literature and art. She used to practice her craft bv making illustrations for fairy tales like Cinderella and Sleeping Beauty. Also drawn to nature, she and her younger brother Walter kept many pets mice, rabbits, even bats and a hedgehog and she loved her family's long holidays in the Scottish countryside and the Lake District, a mountainous area in northwest England. in 19 The As a child and teenager, Potter made great sketches of her pets, as well as of trees and plants. She also kept a diary in which she recorded her Qpinions about cultural and political ideas and events. She wrote in a secret bs nsgst Peri 1866- Code that was not broken until fifteen years after her death. In the 1890s, Potter began selling her drawings.Potter's work was used for Christmas and New Year cards and an illustration of poetry. She was pleased by this success and decided to publish her own illustrated stories for children. In 1901, after the manuscript. was rejected by several publishers, she self-published her first book, The Tale of Peter Rabbit, She had first written and drawn a version of the story in a letter to the. sick child of her former private teacher.、The child was so delighted with it that Potter felt other children would be, too. She was right. The story of naughty Peter, who always gets into trouble because he does not follow his sisters' example and obey his mother's rules, was very popular. 、In 1902, the publisher Frederick Warne & Company printed a commercial edition, and it went on to become one of the most famous children's books of all time 1 Over the next twenty years, Potter wrote and illustrated twenty-two more books with that publisher, her early_observations of the animals and plants of her childhood often making their way into the stories. Potter's The Tale of Mrs. Tiggy-Winkle, published in 1905, for example, includes - 22 -

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