✔ 最佳答案
你好～～～
1) tan∮= 2
(tan∮)^2 = 2^2
(sin∮)^2 / (cos∮)^2 = 4
(sin∮)^2 = 4(cos∮)^2
(sin∮)^2 = 4[1 - (sin∮)^2]
(sin∮)^2 = 4 - 4(sin∮)^2
(sin∮)^2 + 4(sin∮)^2 = 4
5(sin∮)^2 = 4
(sin∮)^2 = 4 / 5
sin∮ = √(4 / 5)
sin∮ = 2 / √5
(sin∮)^2 = 4 / 5
1 - (cos∮)^2 = 4 / 5
(cos∮)^2 = 1 / 5
cos∮ = √(1 / 5)
cos∮ = 1 / √5
2) cos∮= √(11/6)
(cos∮)^2 = 11 / 6
1 - (sin∮)^2 = 11 / 6
(sin∮)^2 = 5 / 6
sin∮ = √(5 / 6)
3) 應該是已知 tan∮ = √(11 / 6) 吧？
tan∮ = √(11 / 6)
(tan∮)^2 = 11 / 6
(sin∮)^2 / (cos∮)^2 = 11 / 6
(sin∮)^2 = 11(cos∮)^2 / 6
6(sin∮)^2 = 11[1 - (sin∮)^2]
6(sin∮)^2 = 11 - 11(sin∮)^2
17(sin∮)^2 = 11
(sin∮)^2 = 11 / 17
sin∮ = √(11 / 17)
(sin∮)^2 = 11 / 17
1 - (cos∮)^2 = 11 / 17
(cos∮)^2 = 6 / 17
cos∮ = √(6 / 17)
4) tan∮ = 4 / 5
sin∮ / cos∮ = 4 / 5
(sin∮)^2 / (cos∮)^2 = (4 / 5)^2
25(sin∮)^2 = 16(cos∮)^2
25(sin∮)^2 = 16[1 - (sin∮)^2]
25(sin∮)^2 = 16 - 16(sin∮)^2
41(sin∮)^2 = 16
(sin∮)^2 = 16 / 41
sin∮= √(16 / 41)
sin∮= 4 / √41
(sin∮)^2 = 16 / 41
1 - (cos∮)^2 = 16 / 41
(cos∮)^2 = 25 / 41
cos∮= 5 / √41
sin∮ * cos∮= 4 / √41 * 5 / √41
= 20 / 41
5) tan∮= 3
sin∮ / cos∮ = 3
(sin∮)^2 / (cos∮)^2 = 9
(sin∮)^2 = 9(cos∮)^2
(sin∮)^2 = 9[1 - (sin∮)^2]
(sin∮)^2 = 9 - 9(sin∮)^2
10(sin∮)^2 = 9
(sin∮)^2 = 9 / 10
sin∮= 3 / √10
(sin∮)^2 = 9 / 10
1 - (cos∮)^2 = 9 / 10
(cos∮)^2 = 1 / 10
cos∮ = √(1 / 10)
cos∮ = 1 / √10
但你的問題好似怪怪的，你給了你 sin∮ 及 cos∮ 的值後，你只要代回去即可～
還有，其實這幾條可以畫一個直角三角形，代回所有邊的數，用勾股定理來求回未知邊，輕鬆的找回答案～～
希望可以幫到你～～～～～
