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Mathematics Senior High

赤線を引いたところの変形がわかりません!

192 ナ 基本 例題 125 三角形の内角の二等分線の長さ(1) 00000 (1)△ABCにおいて,∠A の二等分線が辺 BC と交わる点をDとするとき BD:DC=AB: AC が成り立つことを証明せよ。 (2)△ABCにおいて, BC=6, CA=5, AB=7 とし,∠A の二等分線と辺 BC の交点をDとする。 線分AD の長さを求めよ。 0 CHART OLUTION |基本 117 118 基本130 三角形の内角の二等分線の長さ ① 余弦定理の利用 ② 面積の利用 解答) 三角形の内角の二等分線については,(1)のような性質がある。 これを利用して, (2) では余弦定理を使ってAD の長さを求める。 ②面積の利用は,後で学習する (p.200 基本例題130 参照)。 (1) ∠A=20, ∠ADB=α とすると, △ABD とACD において, 正弦定理により BD AB = sin0 sina' a A 00 180°-α A B D (m) sin(180°-α)=sinα であるから,これらを変形すると DC AC sine sin (180°-α) sin BD= sing AB, DC= sin -AC sina よって C 別解 (1) E Da B A DC 図において, AD // EC と すると,∠AEC=∠BAD (m) - BD: DC=AB: AC =∠CAD=∠ACE AE=AC (2) 線分 AD は ∠A の二等分線であるから,(1)よりよっ BD: DC=AB:AC BC=6, CA=5,AB=7から DC=5/1 △ABCにおいて,余弦定理により cos C= _6252-72__ 12_1 2.6.5 2 A 5 D`--5--C 2・6・5 5 B 7. 2 (mm) 82,a=d △ADCにおいて, 余弦定理により AD2 =52+ 5²+(5)²-2.5.5.1-105 105 AD> 0 であるから AD= 2 4 BD: DC=BA: =AB: AC BD: DC=7:5 から DC=715BC inf. cos は角が大きいほ ど値が小さくなるので,本 問では cos C を求めた。 ← AD’=AC2+DC2 -2AC-DC cos C ASI B

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Mathematics Senior High

tに置き換えずにsin(cos)のまま計算していいのでしょうか?

103190- 34.7= sin34 重要 例題 143 三角比を含む方程式(3) 次の方程式を解け。 *2cos 0+3sin0-3=0(0°M0≦180°) (2) sin Otano= 3 2 (90° <0≦180°) 00000 指針 sino, coso, tan のいずれか1種類の三角比の方程式に直して解く。 sin20+cos20=1やtan0= sino cos 0 を用いて、1つの三角比だけで表す。 (1)はsin0 だけ (2) は cos 0 だけの式になるからその三角比とおく。 →tの2次方程式になる。 ただし, tの変域に要注意! ③tの方程式を解き, tの値に対応する0の値を求める。 基本141 237 CHART 三角比の計算 かくれた条件 sin20+cos20=1が効く (1) cos20=1-sin' 0 であるから 解答 整理すると 2sin20-3sin0+1=0 2 (1-sin20)+3sin0-3 = 0 4 章 01... ① sin=t とおくと, 180°のとき 方程式は 2t23t+1=0 ゆえに (t-1)(2-1)=0 sin0の2次方程式。 出 <おき換えを利用。 YA よって t=1, 2 三角比の拡張 これらは①を満たす。 150° t=1 すなわち sin0=1 を解いて =90°nia- t=1/23 すなわち sing= 11 を解いて0=30°,150° -11 0 √3 1x 2 2 以上から 0=30° 90° 150° 最後に解をまとめる。 sin sin (2) tan= 3 であるから sine.. cos 0 両辺に 2cos を掛ける。 Cos 2 ゆえに 2sin20=-3coso (*) 慣れてきたら, おき換 |えをせずに, (*) から sin20=1-cos' 0 であるから 2 (1-cos20)=-3cOSA (cos0-2) (2cos8+1)=0 整理すると 2cos20-3 cos0-2=0 cosa=t とおくと, 90°も180°のとき -1≦t<0.・・・・・ ① ...... (*) よってcos=2,12 などと進めてもよい。 YA 方程式は2t2-3t-2= ゆえに (t-2)(2t+1)=0 よって t=2, T 1 ①を満たすものはt=- 2 2 TAL 120° 求める解は,t=- 1 1 -1 O 1x すなわち cos0=- を解いて 2 0=120° 2 練習 次の方程式を解け。 8 143 (1) 2sin20-cos0-1=0 (0°≦0≦180°) (2) tan 0=√√2 cos 0 (0°≤0<90°) p.247 EX101

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English Senior High

この文の下から8行目のstream jumping とはどういう訳し方が正解ですか?

B You are reading the following article as you are interested in studying overseas. Summer in Britain Chiaki Suzuki November 2022 This year, I spent two weeks studying English. I chose to stay in a beautiful city, called Punton, and had a wonderful time there. There were many things to do, which was exciting. I was never bored. It can get expensive, but I liked getting student discounts when I showed my student card. Also, I liked window-shopping and using the local library I ate a variety of food from around the world, too, as there were many people from different cultural backgrounds living there. Most of the friends I made were from my English school, so I did not practice speaking English with the locals as much as I had expected. On the other hand, I came to have friends from many different countries/ Lastly, I took public transport/which I found convenient and easy to use as it came frequently. If I had stayed in the countryside, however, I would have seen a different side of life in Britain. My friend who stayed there had a lovely,/relaxing experience. She said farmers sell their produce directly. Also, there are local theatres bands, art and craft shows restaurants, and some unusual activities like stream-jumping. However, getting around is not as easy, so it's harder to keep busy. You need to walk some distance to catch buses or trains, which do not come as often. In fact, she had to keep a copy of the timetables. If I had been in the countryside, I probably would have walked around and chatted with the local people. I had a rich cultural experience and I want to go back to Britain. However, next time I want to connect more with British people and eat more traditional British food. Day 08 2023年度: 共通テスト追試験 第2問B 115

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TOEIC・English Undergraduate

分からないので教えて欲しいです🙇‍♀️

Entrance Exam 否定表現 1. almost 2. I( 1()に入れる最も適切な語句を1~4から選びなさい。 1. I don't think David would make a good leader because he can ( difficult circumstances and tends to give up too quickly. 2. extremely 3. hardly ) go to karaoke, I go only once or twice a year. ) be expected to act honorably in 4. neither (明治大) (芝浦工業大 4. never 1. often 3. Unfortunately, ( seldom ) of the 1. a few 2. few 3. ever passengers escaped injury. 3. many (大阪学院大 推) 4. much 4. ( ) children are born with musical talent. (日本大) 1. none of 2. not all. 3. not every 4. no one 5. ( 2. No 1. as far as 2. far from ) of the workers accepted the director's proposal to cut bonuses. 1. Not 6. The future of English society looked ( 7. I didn't like the food at that restaurant. It was (. (東海大 3. Never ) promising in the 1840s. None (立命館大) 3. for far 4. too far ) delicious. (福岡大) 1. anything but 2. nothing but 3. without 4. out of 8. He was so drunk that he could ( ) walk. (大阪学院大) 9. 1. all 1. able 2. unable This train doesn't stop at ( a few 3. hard 4. hardly ) station. 大阪商業大推) 2. 3. little 4. every 2. few 12. " Can 10. The latest model of this mobile phone is ( 1. not seldom 3. all not 11. Before I watched the documentary, I knew ( 1. little à you come to the party tonight?" "( 1. Yes, I can ) easy to use. (獨協大) 2. not necessarily 4. ever not 3. seldom ) about life under the sea. 4. hardly (東京工科大) ). I have a lot of homework." (拓殖大) 2. Yes, I do 3. No, I'm afraid not 13. Japan has ( 1. a little 2. few 4. No, I hope not ) oil and therefore is almost entirely dependent on imports. (センター) 3. little 4. small

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