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# Trigonometry

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### Trigonometry

1. 1. TRIGONOMETRY
2. 2. TRIGONOMETRIC FORMULA FOR SUM ANDDIFFERENCE OF TWO ANGLES cos (A + B) = cos A . cos B – sin A . sin B cos (A – B) = cos A . cos B + sin A . sin B sin (A + B) = sin A . cos B + cos A . sin B sin (A – B) = sin A . cos B – cos A . sin B example cos (3a + 2b) = ? cos 3a . cos 2b – sin 3a . sin 2b cos 75 = ? cos 75 = cos (30 + 45) cos 30 . cos 45 – sin 45 . sin 30 =
3. 3.  Given that cos α = 3/5 and cos β = 12/13. α and β angles are acute. Find the value of : a. cos ( α + β ) b. cos ( α – β ) Given that sin A = 5/13 and cos B = 3/5. A and B angles are acute. Prove that sin (A + B) = 63/65 ? Diketahui cos (A + B) = 2/5 dan cos A cos B = ¾. Tentukan nilai tan A . tan B ? answer : 7/15 Diketahui A dan B adalah sudut lancip, cos(A – B) = dan cos A . cos B = 1/2 , tentukan nilai dari answer :
4. 4.  The formula for tan (A + B) and tan (A – B) example tan 15 = ? tan 15 = tan (45 – 30) = = tan 75 = ? answer :
5. 5. TRIGONOMETRIC FORMULA OF MULTIPLEANGLES Soal UN tahun 2009/2010 IPA diketahui sin A – cos A = 2p. Nilai sin 2A = ? a. 1-2p2 d. 4p2-1 b. 1-4p2 e. 2p -1 c. 2p2-1 answer : 1 – 4p2
6. 6. HOMEWORK Diketahui tan A = -3/4 dan tan B = 15/8. Sudut A tumpul dan sudut B lancip. Tentukan nilai dari : a. cos ( α + β ) b. cos ( α – β ) Soal UN tahun 2009/2010 IPA Diketahui (A + B) = /3 dan sin A sin B = ¼ . Nilai dari cos (A – B) = … answer : 1 If sin x = 3/5, than determine the value of cos 2x ? answer : 7/25 Jika sin x – cos x = p maka harga dari sin 2x ? answer : 1 – p2
7. 7. MULTIFICATION FORMULA Tanpa menggunakan kalkulator, hitunglah nilai : 2 sin 75 sin 15 = ? cos 80 cos 40 = ?Answer : 2 sin 75 sin 15 = cos (75 – 15) – cos (75 + 15) = = cos 60 – cos 90 = ½ - 0 = ½ cos 75 cos 15 = ½ (cos (75 + 15) + cos (75 – 15) = = ½ (cos 90 + cos 60) = ½ (0 + ½) = ¼
8. 8. SUM AND DIFFERENCE FORMULA sin 3p + sin p = ? ? a. tan x d. cot 2x b. cot x e. tan 6x c. tan 2x
9. 9. HOMEWORK Prove : 2 sin 3A sin 4A + 2 cos 5A cos 2A – cos 3A = cos A ? a. tan 2x d. tan 8x b. tan 4x e. tan 16x c. tan 6x sin (3x + 2y) = 1/3 dan cos (3x – 4y) = ¾ tentukan