1. Trigonometry 2 PART

2. SINE

3. SINE FUNCTION Opposite Hypotenuse SinΘ=

4. Sine is used for finding the adjacent side or angle of a triangle. The sine of an angle is the ratio of the opposite side over the hypotenuse.

5. Sin70 0 (22) = x 20.7 = x x= 20.7 m 70 o 22m x=? hyp adj opp Sin Θ = opposite hypotenuse Sin 70 o = x 22

6. SINE LAW b Sin B = Sin B B c Sin C Sin A A a Sin A Sin C C = = = OR C c a A b B

7. We use Sine Law if we are given an angle, side, and angle (ASA) or 2 sides and an angle (SSA). The Sine Law is used for non right angle triangles to find the missing sides or angles. g g g ASA g g g SSA

8. EXAMPLE

9. c a=6 b=x C B=32 o A=68 o b Sin 32 = 6 Sin 68 b= 6 Sin 68 (Sin 32) b= 3.4 cm

10. COSINE

11. COSINE FUNCTION Adjacent Hypotenuse CosΘ=

12. The cosine function is used to find the opposite side or angle of a right triangle. The cosine of an angle is the ratio of the adjacent side over the hypotenuse.

13. x=48.2 o hyp x 30m 20m opp adj Cos Θ = adjacent hypotenuse Cos x = 20 30 Cos -1 = 20 30

14. a 2 =b 2 +c 2 -2bc(CosA) b 2 =a 2 +c 2 -2ac(CosB) c 2 =a 2 +b 2 -2ab(CosC) COSINE LAW C c a A b B

15. Cosine Law is used when we are given 3 pieces of information but there isn’t any opposite sides or angles. We can use cosine law if we have 2 sides and an angle (SAS) or 3 sides (SSS) SAS SSS g g g g g g

16. EXAMPLE

17. b 2 =a 2 +c 2 -2ac(CosB) b 2 =6 2 +4 2 -2(6)(4)(Cos50) b 2 =36+16-48(Cos50) b 2 =√21.1 b=4.6 cm B=50 o C C=4 A a=6 b=x

18. SOLVING A TRIANGLE

19. c 2 =a 2 +b 2 -2ab(CosC) 8 2 =6 2 +7 2 -2(6)(7)(CosC) 64=36+49-84(CosC) 64=85-84(CosC) -21=-84(CosC) -21/84-=CosC Cos-1(-21/-84) C=75.5 o A=180-75.5-58 A=46.5 o B = 58 o Step 1 Step 2 Step 3 Sin 75.5 8 = Sin B 7 ( Sin 75.5 8 ) Sin -1 7 6 8 7 C A B

20. THE END BY: Novelyn Binas Ashlee Thomas Daniel Lim Mark Estrada Julie Anne Navea