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Mathematics Senior High

149.2 tanθを求める過程に問題はないですか? またcosθを求める過程はこれだとダメですよね?? (cosθ>0とは限らないのにそうだと決めつけて計算してしまっているように振り返った時に感じた。)

234 基本例題 149 2倍角、半角の公式 (1) << sin π (2) t=tan 解答 7/<0< 2 指針 (1) 2倍角、半角の公式を利用する。 また sin 20, tan- 209 ゆえに 0 のとき、次の等式が成り立つことを証明せよ。 2 18000 182 sin0= (1) cos20=1-2sin²0=1-2・ << πであるから よって cos 20, sin20, tan =12123のとき, 5 の値を求めるには, Coseの 必要になるから,かくれた条件 sin'0+cos²0=1 を利用して,この値も求めて 0 (2) 0=2. であるから, 2倍角の公式を利用。 tan0→cosl sin0 の順に証明する tan と cose が示されれば, sin は sin0=tan Acose により示される 。 tan 2t 1+t², (2) tan 0=tan 2. cos0=-√1-sin20 = 0 2 0 2 sin20=2sinAcos0=2. <0よりであるから 2 1 1+tan²= 0 S2. 2 COS よって cos0=cos2・ 1-cos 1+cos 0 2 tan から cos0= 1-tan²- 31² 5 0 2 0 2 20 2 ゆえに sin0=tanocos0= = COS 2 =2cos' --√√₁-(²³)² = 2.³-·-(-3) = -4/5 5 5 25 =1- 0 2 2t 1-t² 0 2 1-t² 2t tan0= 1+2, can 1-t² = 18 7 leden 20 25 25 BAJAR com 5+4 5-4 -1= = 0 tan o na 2 2ie-4 ata and 5 n 424 s 2t 1-t² 1-12 1+12 =3 (t≠±1) 1 + tan[] 2 1+ t² 0 2 ->0 2t 1+t² 191/202 -1= の値を求めよ。 200 1 1+t2 1-t² 1+t² (t≠±1) S=phieS+1=S p. 233 L は第2象限の角であるか 5 cos 0<0 1+ 1- 検討 sin=scos 2 5+4 5-4 COS10/2=cとおり と 0 tan-2-1-2 これを式の右辺に代入して ps2+cz = 1 などから、左 導くこともできる。

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English Senior High

「,well behind 」の部分の構造、意味を教えてください。

[Review] Back in the late sixties, thinkers on both sides of the Atlantic were troubled by problems which may seem strange to us today: they were worried that the leisure age which they believed was fast approaching would leave people with too much time on their hands. They were worried that the work ethic was losing its grip on a new rebellious generation and they pondered how they would motivate people to work. They needn't have worried. The much-predicted "leisure age" promised by technology has not materialized. In fact, quite the reverse: people are working harder than ever. There is less leisure time and, most surprising of all, the very workers with the greatest bargaining power are choosing to work the hardest. The problem is the burnout of white- collar Britain. For over a century, the average number of hours spent working over a lifetime slowly declined in Britain. The historian James Arrowsmith has calculated that in 1856 our ancestors put in 124,000 hours over a 40-year working life and, by 1981, it was 69,000. There it remained for a decade, but in the early nineties it began to increase again. On average full-time British workers now put in 80,224 hours over their working life, and that figure rises to 92,000 for those on a 50-hour week, which is common among the self- employed, the skilled, and professional and managerial workers. Many are working the kind of hours that would have been familiar to factory workers in the middle of the 19th century. The only difference is that now it's the bosses who are more likely to be putting in the hours than those on the shop floor. Britain has followed a US model of all work, no play, in contrast to continental Europe. Full-time workers in Britain now work the longest hours in Europe an average of 43.6 hours per week compared with an EU average of 40.3. Even more marked is the difference in holidays between Britain and continental Europe; the UK has, on average, 28 days a year, well behind France with 47, Italy with 44 and Germany with 41. Add the difference in weekly hours and holidays and it amounts to the British working almost eight weeks a year more than their European counterparts. -

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