a) a - jedna przyprostokątna = 9 b - druga przyprostokątna = 12 c - przeciwprostokątna = ? -------------------------------------- c = √(a² + b²) = √(9² + 12²) = √(81 + 144) = √225 = 15 sinα = a/c = 9/15 = 3/5 cosα = b/c = 12/15 = 4/5 tgα = a/b = 9/12 = 3/4 ctgα = b/a = 12/9 = 4/3 sinβ = b/c = 12/15 = 4/5 cosβ = a/c = 9/15 = 3/5 tgβ = b/a = 12/9 = 4/3 ctgβ = a/b = 9/12 = 3/4 ----------------------------------------- b) a = 4 b = 5 c = √(a² + b²) = √(4² + 5²) = √(16 + 25) = √41 sinα = a/c = 4/√41 = 4√41/41 cosα = √41/5 tgα = a/b = 4/5 ctgα = b/a = 5/4 sinβ = b/c = 5/√41 = 5√41/41 cosβ = a/c = 4/√41 = 4√41/41 tgβ = b/a = 5/4 ctgβ = a/b = 4/5 ------------------------------------------- c) a = 1 b = 5 c = √(a² + b²) = √(1 + 5²) = √(1 + 25) = √26 sinα = a/c = 1/√26 = √26/26 cosα = b/c = 5/√26 = 5√26/26 tgα = a/b = 1/5 ctgα = b/a = 5/1 = 5 sinβ = b/c = 5/√26 = 5√26/26 cosβ = a/c = 1/√26 = √26/26 tgβ = b/a = 5/1 = 5 ctgβ = a/b = 1/5
