1.
cosa = 0,8 = 8/10 = 4/5
sin²a + cos²a = 1
sin²a + (4/5)² = 1
sin²a = 1 - 16/25
sin²a = 9/25
sina = 3/5
tga = sina / cosa = 3/5 : 4/5 = 3/5 * 5/4 = 3/4
ctga = cosa / sina = 4/5 : 3/5 = 4/5 * 5/3 = 4/3
2.
cosa = 3/5
sin²a + cos²a = 1
sin²a + (3/5)² = 1
sin²a = 1 - 9/25
sin²a = 16/25
sina = 4/5
tga = sina / cosa = 4/5 : 3/5 = 4/5 * 5/3 = 4/3
ctga = cosa / sina = 3/5 : 4/5 = 3/5 * 5/4 = 3/4
3.
cosa = 3/2 <----- coś nie tam, bo cosa nie moze takiej wartości posiadac
4.
ctga = 4/5
tga = 1 / ctga = 1 : 4/5 = 1 * 5/4 = 5/4
sina / cosa = tga
sina / cosa = 5/4
5cosa = 4sina
cosa = 4/5 sina
sin²a + cos²a = 1
sin²a + (4/5sina)² = 1
sin²a + 16/25sin²a = 1
41/25sin²a = 1
sin²a = 25/41
sina = 5/√41
sina = 5√41 / 41
cosa = 4/5 * 5√41 / 41
cosa = 4√41/ 41
cosα = 0,8
sin²α + cos²α = 1
sin²α + 0,8² = 1
sin²α + 0,64 = 1
sin²α = 0,36
sinα = 0,6
tgα = sinα/cosα
tgα = 0,6/0,8 = 0,75
ctgα = 1/tgα
ctgα = 1/0,75 = 4/3
cosα = 3/5
9/25+ sin²α = 1
sin²α = 6/25
sinα = √6/5
tgα = √6/5 / 3/5 = √6/3
ctgα = 1/√6/3 = 3/√6 = 3√6/6 = √6/2
cosα = 3/2 - sprzeczność
ctgα = 4/5
tgα = 5/4
sinα/cosα = 5/4
5cosα = 4sinα => sinα = 5/4cosα
cos²α + 25/16cos²α = 1
41/16cos²α = 1
cos²α = 16/41
cosα = 4/√41 = 4√41/41
sinα = 5/4 * 4√41/41 = 5√41/41
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