{"paper":{"id":"site-2680","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"podstawowa","variant":null,"exam_pdf":null,"key_pdf":null,"question_count":7,"source_label":"Matematyka · Zbiory zadań (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},"questions":[{"id":"site-2680/zad/2386","paper_id":"site-2680","number":"2386","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"podstawowa","text":"Zadanie z trygonometrii: Oblicz a-b, gdy a = sin^4a - cos^4a, b = 1 - 4 sin^2a cos^2a dla a = 60 stopni.","answer":null,"answer_text":null,"solution":null,"image":"img/site/2680/zad-2386.svg","solution_image":"img/site/2680/rozw-2386.svg","topics":null,"page_from":null,"source":"site","answer_source":null,"answer_text_source":null,"solution_source":null,"text_source":"site","source_label":"Matematyka · Zbiory zadań (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-2680/zad/3029","paper_id":"site-2680","number":"3029","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"podstawowa","text":"Wiedząc, że alfa jest kątem ostrym i tg alfa = 2, oblicz wartość wyrażenia {4 cos alfa - 3 sin alfa / 3 cos alfa + 5 sin alfa}","answer":null,"answer_text":null,"solution":null,"image":"img/site/2680/zad-3029.svg","solution_image":"img/site/2680/rozw-3029.svg","topics":null,"page_from":null,"source":"site","answer_source":null,"answer_text_source":null,"solution_source":null,"text_source":"site","source_label":"Matematyka · Zbiory zadań (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-2680/zad/3051","paper_id":"site-2680","number":"3051","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"podstawowa","text":"W pewnym trójkącie prostokątnym suma cosinusów kątów ostrych jest równa 2 pierwiastek z 3 / 3. Oblicz iloczyn sinusów tych kątów.","answer":null,"answer_text":null,"solution":null,"image":"img/site/2680/zad-3051.svg","solution_image":"img/site/2680/rozw-3051.svg","topics":null,"page_from":null,"source":"site","answer_source":null,"answer_text_source":null,"solution_source":null,"text_source":"site","source_label":"Matematyka · Zbiory zadań (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-2680/zad/3206","paper_id":"site-2680","number":"3206","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"podstawowa","text":"W trójkącie prostokątnym przyprostokątne mają długość 2 i 4, a jeden z kątów ostrych ma miarę alfa. Oblicz sin alfa * cos alfa.","answer":null,"answer_text":null,"solution":null,"image":"img/site/2680/zad-3206.svg","solution_image":"img/site/2680/rozw-3206.svg","topics":null,"page_from":null,"source":"site","answer_source":null,"answer_text_source":null,"solution_source":null,"text_source":"site","source_label":"Matematyka · Zbiory zadań (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-2680/zad/3207","paper_id":"site-2680","number":"3207","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"podstawowa","text":"Kąt alfa jest ostry i sin alfa = 1/4. Oblicz 3+2tg^2alfa.","answer":null,"answer_text":null,"solution":null,"image":"img/site/2680/zad-3207.svg","solution_image":"img/site/2680/rozw-3207.svg","topics":null,"page_from":null,"source":"site","answer_source":null,"answer_text_source":null,"solution_source":null,"text_source":"site","source_label":"Matematyka · Zbiory zadań (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-2680/zad/5331","paper_id":"site-2680","number":"5331","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"podstawowa","text":"Kąt α jest ostry i spełnia warunek 2sinα + 3cosα / cosα = 4. Oblicz tangens α.","answer":null,"answer_text":null,"solution":null,"image":"img/site/2680/zad-5331.svg","solution_image":"img/site/2680/rozw-5331.svg","topics":null,"page_from":null,"source":"site","answer_source":null,"answer_text_source":null,"solution_source":null,"text_source":"site","source_label":"Matematyka · Zbiory zadań (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-2680/zad/5495","paper_id":"site-2680","number":"5495","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"podstawowa","text":"Rozwiązanie zadania. Kąt α jest ostry i sinα + cosα = 7/5. Oblicz wartość wyrażenia 2sinαcosα.","answer":null,"answer_text":null,"solution":null,"image":"img/site/2680/zad-5495.svg","solution_image":"img/site/2680/rozw-5495.svg","topics":null,"page_from":null,"source":"site","answer_source":null,"answer_text_source":null,"solution_source":null,"text_source":"site","source_label":"Matematyka · Zbiory zadań (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"}]}