1.oblicz wartość pozostałych funkcji sin x=2/3 2.sprawdź tożsamość (sinx+cosx)^+(sinx-cosx)^=2
sinx = 2/3
sin²x + cos²x = 1
(2/3)² + cos²x = 1
cos²x = 1 - 4/9
cos²x = 5/9
cosx = √5 / 3 lub cosx = - √5 / 3
tgx = sinx / cosx
tgx = 2/3 : √5 / 3 = 2/3 * 3 / √5 = 2 / √5 = 2√5 / 5
lub
tgx = 2/3 : (-√5 / 3 )= 2/3 * (-3 / √5) = - 2 / √5 = - 2√5 / 5
ctgx = 1 / tgx = 1 : 2 / √5 = 1 * √5 / 2 = √5 / 2 lub ctgx = - √5 / 2
2.
(sinx + cosx)² + (sinx - cosx)² = 2
L = sin²x + 2sinxcosx + cos²x + sin²x - 2sinxcosx + cos²x = 2sin²x + 2cos²x = 2(sin²x + cos²x) = 2 * 1 = 2 = P
Rozwiązanie w załączniku
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sinx = 2/3
sin²x + cos²x = 1
(2/3)² + cos²x = 1
cos²x = 1 - 4/9
cos²x = 5/9
cosx = √5 / 3 lub cosx = - √5 / 3
tgx = sinx / cosx
tgx = 2/3 : √5 / 3 = 2/3 * 3 / √5 = 2 / √5 = 2√5 / 5
lub
tgx = 2/3 : (-√5 / 3 )= 2/3 * (-3 / √5) = - 2 / √5 = - 2√5 / 5
ctgx = 1 / tgx = 1 : 2 / √5 = 1 * √5 / 2 = √5 / 2 lub ctgx = - √5 / 2
2.
(sinx + cosx)² + (sinx - cosx)² = 2
L = sin²x + 2sinxcosx + cos²x + sin²x - 2sinxcosx + cos²x = 2sin²x + 2cos²x = 2(sin²x + cos²x) = 2 * 1 = 2 = P
Rozwiązanie w załączniku