Mathematics is a language that all understand ?

1. Тригонометрични функции на обобщен ъгъл Trigonometric functions of the generalized angle

2. Град y си 0° 30° 45° 60 ° 90 ° 120 ° 135 ° 150 ° 180 ° 270 ° 360 ° Радиани Radians 0 π 6 π 4 π 3 π 4 2 π 3 3 π 4 5 π 6 π 3 π 2 2 π

5. sin(150 ° )= sin150 ° = 1 tg(60 ° ) = tg60 ° = √3 2 cos(135 ° ) = cos135 ° = -√2 cotg(90 ° ) = cotg90 ° = 0 2 sinα = a cosα = b tgα = a cotgα = b c c b a sinβ = b cosβ = a tgβ= b cotgβ= a c c a b

6. Sin(90°-α) = cosα Cos(90°-α) = sinα Tg(90°-α) = cotgα Cotg(90°-α) = tgα Sin(90°+α)=cosα Cos(90°+α)=-sinα Tg(90°+α)=-cotgα Cotg(90°+α)=-tgα Sin(180°-α)=sinα Cos(180°-α) = - cosα Tg(180°-α)=-tgα Cotg(180°-α)=-cotgα Sin(180°+α )=- sinα Cos(180°+α)=-cosα Tg(180°+α)=tgα Cotg(180°+α)=cotgα Sin(270°-α)=-cosα Cos(270°-α)=-sinα Tg(270°-α)=cotgα Cotg(270°-α)=tgα Sin(270°+α)=-cosα Cos(270°+α)=sinα Tg(270°+α)=-cotgα Cotg(270°+α)=-tgα

7. sin300° = sin(30 °+270 °) = sin30 ° = 1 2 cos240° = cos(60°+180°) = cos60°= 1 2 tg(-1410° ) = -tg(3x360°+330°) = -tg330° = = -tg(-30°+ 360 °) = tg30° = √3 3 cotg(750°) = cotg(30°+2.360°) = cotg30° = = √3

16. √ √ √ √ √

17. √ 1- √ √ √ √

19. sinα + sinβ = 2sin α + β cos α – β 2 2 sinα - sin β = 2sin α - β cos α + β 2 2 cosα + cos β = 2cos α + β cos α - β 2 2 cosα - cos β = -2sin α + β sin α - β 2 2 Sinα.cos β = 1 [sin(α- β ) +sin(α+ β )] 2 Cosα.cos β = 1 [cos(α- β ) + cos(α+ β )] 2 Sinα.sin β = 1 [cos(α- β ) – cos(α+ β )] 2

24. 1+cos2α + sin2α = cos0° + cos2α + sin2 α = = 2cos 0°+2 α cos 0°- 2 α + sin2 α = 2 2 =2cos α .cos α + 2sin α .cos α = =2cos α (cos α + sin α ) = =2cos α .2cos α + 90° - α cos α – 90° - α = 2 2 =4cos α .cos45°.cos (90° - 2 α ) = 4.√2 cos α .sin α = 2√2 cos α sin2 α 2

25. Created by: Vladislav Denev Tihomir Jelev Magdalena Veleva Desislava Petrova SOU "Jeleznik" Stara Zagora Bulgaria