Odpowiedź:
a)
tgα = 2
tg²α = 2² = 4
sin²α/cos²α = 4
sin²α = 4cos²α
1 - cos²α = 4cos²α
1 = 4cos²α + cos²α = 5cos²α
cos²α = 1/5
cosα = √(1/5) = 1/√5 = √5/5
sin²α + cos²α = 1
sin²α = 1 - cos²α = 1 - (√5/5)² = 1 - 5/25 = 1 - 1/5 = 4/5
sinα = √(4/5) = 2/√5 = 2√5/5
ctgα = 1/tgα = 1/2
b)
sinα = 0,4
sin²α = (0,4)² = 0,16
1 - cos²α = 0,16
cos²α = 1 - 0,16 = 0,84 = 84/100 = 42/50 = 21/25
cosα = √(21/25) = √21/5
tgα = sinα/cosα = 4/10 : √21/5 = 4/10 * 5/√21 = 4/2 * 1/√21 = 2/√21 = 2√21/21
ctgα = 1/tgα = 21/2√21 = 21√21/(2 * 21) = 21√21/42 = √21/21
