{"id":"informator-maturalny-matematyka-2010/zad/66","paper_id":"informator-maturalny-matematyka-2010","number":"66","points":2,"ptype":"open","subject":"matematyka","category":"informator-maturalny","year":2010,"month":null,"level":null,"text":"Zadanie 66. (2 pkt)\nKąt α jest ostry i\n1\nsin\n4\nα =\nOblicz\n2\n3\n2tg α","answer":null,"answer_text":null,"solution":"sinα=1/4, α ostry, więc cos^2α=1-1/16=15/16, cosα=sqrt(15)/4.\ntgα=sinα/cosα=(1/4)/(sqrt(15)/4)=1/sqrt(15), tg^2α=1/15.\n3+2tg^2α = 3+2/15 = 45/15+2/15 = 47/15.\nOdpowiedź: 47/15.","image":"img/informator-maturalny-matematyka-2010/zad-66.webp","solution_image":null,"topics":null,"page_from":85,"source":"ai","answer_source":null,"answer_text_source":null,"solution_source":"ai","text_source":"ocr","source_label":"Matematyka · Informator maturalny · 2010","subject_label":"Matematyka","category_label":"Informator maturalny","text_html":"<p>Zadanie 66. (2 pkt)<br>Kąt α jest ostry i<br>1<br>sin<br>4<br>α =<br>Oblicz<br>2<br>3<br>2tg α</p>","solutions":[{"source":"ai","label":"AI","kind":"text","html":"<p>sinα=1/4, α ostry, więc cos^2α=1-1/16=15/16, cosα=sqrt(15)/4.<br>tgα=sinα/cosα=(1/4)/(sqrt(15)/4)=1/sqrt(15), tg^2α=1/15.<br>3+2tg^2α = 3+2/15 = 45/15+2/15 = 47/15.<br>Odpowiedź: 47/15.</p>"}]}