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Trigonometry
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- 3. 3 Sin(a + b)= sin a . cos b + cos a . Sin b Sin(a - b) = sin a . cos b – cos a . Sin b Rumus jumlah dan selisih dua sudut Cos(a + b) = cos a . cos b – sin a . Sin b Cos(a - b) = cos a . cos b + sin a . Sin b
- 4. 4 tan(α + β)= tan(α - β) = βα βα tan.tan1 tantan − + βα βα tan.tan1 tantan + −
- 5. 5 Rumus Sudut Rangkap Sin2a = 2 sin a . Cos a Cos 2a = asinacos 22 − asinacos 22 − Cos 2a = 1acos2 2 − Cos 2a = asin21 2 − A B C tan 2a = atan1 atan2 2 −
- 6. Rumus Sudut Setengahan sina = 2 acos1− ±A B C tan a = 2 1 cos a =2 1 2 acos1+ ± 2 1 acos1 asin asin acos1 acos1 acos1 + = − = + − ±
- 7. 7 Rumus jumlah dan selisihsin dan cos )ba( 2 1 sin).ba( 2 1 sin2bsinasin −+=+ )ba( 2 1 sin).ba( 2 1 cos2bsinasin −+=− )ba( 2 1 cos).ba( 2 1 cos2bcosacos −+=+ )ba( 2 1 sin).ba( 2 1 sin2bcosacos −+−=−
- 8. 8 Rumus perkalian sin dancos 2 sin a . cos b = sin (a + b) + sin (a – b) 2 cos a . sin b = sin (a + b) – sin (a – b) 2 cos a . cos b = cos (a + b) + cos (a – b) – 2 sin a . sin b = cos (a + b) – cos (a – b)
- 9. S + S S– S C + C C - C Menghafal Rumus 2 S C 2 C S 2 C C – 2 S S + 2 1 − 2 1 + – )ba( 2 1 cos).ba( 2 1 sin2bsinasinSC2SS −+=+→=+ )ba(sin)ba(sinbcos.asin2SSCS2 −++=→+=
- 10. 10 1. Sin 75o =…. Answer : sin750 = sin(450 + 300 ) = sin450 cos300 + cos450 sin300 = ½√2.½√3 + ½√2.½ = ¼√6 + ¼√2 = ¼√2(√3 + 1) Example : Remember : sin(α + β) = sinα.cosβ + cosα.sinβ
- 11. 11 2. Diketahui sinA = cos B = A dan B adalah sudut-sudut lancip sin(A – B) =…. Bahasan: sin(A – B)= sin A cos B – cos A sin B sin A = cosA = 5 3 25 7 ? ? 5 3 A 3 5 4 5 4 B cos B = sin B = 25 7 7 25 24 25 24
- 12. 12 sin(A – B)= sin A cos B – cos A sin B = x - x = = 5 3 25 7 5 4 25 24 125 96 125 21 − 5 3 125 75 −=−
- 13. 13 Solve: cos α cosβ + sin α sin β = cos (α - β) = = = ....sinsincoscos 28 13 7 5 28 13 7 5 =+ ππππ =+ 28 13 7 5 28 13 7 5 sinsincoscos ππππ )cos( 28 13 7 5 ππ − )(cos 28 7π )(cos 4 π 2 2 1
- 14. 14 1. tan 105°= …. Solve : tan105° = tan(60° + 45°) oo oo 45tan.60tan1 45tan60tan − + = 1.31 13 − + = x 31 31 − + = 31 31 + +
- 15. 15 tan 105° =x = = = = -2 - √3 31 31 − + 31 31 + + 31 )31( 2 − + 31 3321 − ++ 2 324 − +
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