Odpowiedź:
a)
cosα = 2/5
cos²α =(2/5)² = 4/25
1 - sin²α = 4/25
sin²α = 1 - 4/25 = 21/25
sinα = √(21/25)= √21/5
tgα = sinα/cosα = √21/5 : 2/5 = √21/5 * 5/2 = √21/2
ctgα = 1/tgα = 2/√21 = 2√21/21
b)
tgα = 3
tg²α = 3² = 9
sin²α/cos²α = 9
sin²α = 9cos²α = 9(1 - sin²α) = 9 - 9sin²α
sin²α + 9sin²α = 9
10sin²α = 9
sin²α = 9/10
sinα = √(9/10) = 3/√10 = 3√10/10
sinα/cosα =3
3√10/10 : cosα = 3
3√10/10 = 3cosα
cosα = 3√10/10 : 3 = 3√10/10 * 1/3 = 3√10/30 = √10/10
tgα = 3
ctgα = 1/tgα = 1/3
Szczegółowe wyjaśnienie:
do obliczeń wykorzystano wzory :
sin²α + cos²α = 1
sin²α = 1 - cos²α
cos²α = 1 - sin²α
tgα = sinα/cosα
ctgα = 1/tgα
