7.
б) cos α= -√6 π < α < π (2 четверть) sinα: "+"<br> 4 2 tgα и ctgα: "-"
sinα=√1-cos²α=√1-(√6/4)²=√1-(6/16)=√(10/16)=√10 = √10
√16 4
tgα= sinα = √10 : (-√6) = - √10 = - √2*√5 = -√5*√3 = -√15
cosα 4 4 √6 √2*√3 3 3
ctgα=1/tgα=- 3 = -3*√15 = -√15
√15 15 5
в) sinα=√2 0 < α < <u>π (1 четверть) cosα, tgα, ctgα : "+"
3 2
cosα=√1-sin²α=√1-(√2/3)²=√1-(2/9)=√(7/9)=√7=√7
√9 3
tgα=sinα = √2 : √7 = √2 = √2*√7 =√14
cosα 3 3 √7 7 7
ctgα=1/tgα= 7 = 7√14 = √14
√14 14 2
г) cosα=15 3π < α < 2π (4 четверть) sinα, tgα, ctgα: "-"<br> 17 2
sinα= - √1-cos²α= - √1-(15/17)²= - √1-(225/289)= - √(64/289)= - 8
17
tgα=sinα=- 8 : 15 = - 8
cosα 17 17 15
ctgα=1/tgα=- 15
8