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Menyelesaikansoal-soal yang berkaitandengan jumlah dan selisih sudutserta sudut rangkaphttp://meetabied.wordpress.com

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Rumusjumlah dan selisih dua sudut

sin( + ) = sin.cos + cos.sin sin( - ) = sin.cos - cos.sinhttp://meetabied.wordpress.com

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1. Sin 75o = . Bahasan: sin( + ) = sin.cos + cos.sin sin750 = sin(450 + 300) = sin450cos300 + cos450sin300 = 2.3 + 2. = 6 + 2 = 2(2 + 1)http://meetabied.wordpress.com

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2. Diketahui sin A = cos B = A dan B adalah sudut-sudut lancip sin(A B) =. Bahasan: sin(A B)= sinAcosB cosAsinB sinA = cosA = ??354cos B =sin B =72524http://meetabied.wordpress.com

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sin A = cos A = cos B = sin B =sin(A B) =. = sinAcosB cosAsinB = x - x = = http://meetabied.wordpress.com

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Rumusjumlah dan selisih dua sudut cos( + ) = coscos - sinsin cos( - ) = coscos + sinsinhttp://meetabied.wordpress.com

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1. Bahasan: coscos + sinsin = cos( - )

=

= =http://meetabied.wordpress.com

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2. a. sina.sinb b. cosa.cosb c. sina.sinb d. 1 tana.tanb e. 1 + tana.tanb http://meetabied.wordpress.com

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= = 1 tana.tanb jawab dhttp://meetabied.wordpress.com

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3. Tentukan nilai cos56 + sin56.tan28 Bahasan: cos56 + sin56.tan28 = cos56 + sin56. = cos56 +http://meetabied.wordpress.com

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= cos56 + = = =Jadi, Nilai cos56 + sin56.tan28 = 1 = 1http://meetabied.wordpress.com

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4. Pada suatu segitiga siku-siku ABC berlaku cosA.cosB = . Maka cos(A B) =. Bahasan: siku-siku ABC; cosA.cosB = maka ABC siku-siku di C C = 90 A + B + C = 180 A + B = 90 http://meetabied.wordpress.com

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A + B + C = 180 A + B = 90 A = 90 B B = 90 Acos(A B) = cosA.cosB + sinA.sinB = + sin(90 B).sin(90-A) = + cosB.cosA = + = 1Jadi cos(A B) = 1 http://meetabied.wordpress.com

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Rumusjumlah dan selisih dua sudut

tan( + ) =

tan( - ) = http://meetabied.wordpress.com

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1. tan 105 = . Bahasan: tan105 = tan(60 + 45) http://meetabied.wordpress.com

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tan 105 = x = = = = -2 - 3 http://meetabied.wordpress.com

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2. Diketahui A + B = 135 dan tan B = . Nilai tan A= . Bahasan: A + B = 135 tan(A + B) = tan 135 = -1 = -1 http://meetabied.wordpress.com

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= -1 tan A + = -1 + tan A tan A - tan A = -1 - tan p = -1 Jadi, tan p = -3 http://meetabied.wordpress.com

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3. Jika tan q = dan p q = maka tan p = . Bahasan: p q = tan(p q) = tan = 1 = 1 http://meetabied.wordpress.com

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= 1 tan p - = 1 + tan p tan p - tan p = 1 + tan p = 1 Jadi, tan p = 3 http://meetabied.wordpress.com

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Rumus Sudut Rangkap sin2a = 2 sina.cosacontoh: 1. sin10 = 2sin5.cos5 2. sin6P = 2sin3P.cos3P 3. sin t = 2sint.cost http://meetabied.wordpress.com

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Diketahui cos = Nilai sin 2 =. Bahasan: cos = sin =

435http://meetabied.wordpress.com

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cos = sin =

Jadi sin2 = 2sin.cos = 2. x = 435http://meetabied.wordpress.com

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2. Jika tan A = maka sin 2A =. Bahasan: tan A = sinA = dan cosA = sin2A = 2 sinA.cosA = 2 x x = 12http://meetabied.wordpress.com

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3. Jika sinx cosx = p maka harga sin 2x =. Bahasan: sinx cosx = p (sinx cosx)2 = p2 sin2x 2sinx.cosx + cos2x = p2 http://meetabied.wordpress.com

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sin2x 2sinx.cosx + cos2x = p2sin2x + cos2x 2sinx.cosx = p2 1 sin2x = p2 1 p2 = sin2x

Jadi, harga sin2x = 1 p2 http://meetabied.wordpress.com

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4. Diketahui A adalah sudut lancip dan cosA = Nilai sin A = . Bahasan: cosA = dengan phytagoras t2 = 2x (x + 1) t = x - 1 x+ 12xt = x - 1http://meetabied.wordpress.com

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cosA = sinA =sinA = 2sinA.cosA = 2 x x = Jadi, sin2x = x+ 12xt = x - 1http://meetabied.wordpress.com

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Rumus Sudut Rangkap

cos 2a = cos2a sin2a = 2cos2a 1 = 1 2sin2a http://meetabied.wordpress.com

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Diketahui cos = maka cos 2 =. Bahasan: cos2 = 2cos2 - 1 = 2( )2 1 = - 1 = - http://meetabied.wordpress.com

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2. Diketahui sinx = maka cos 2x =. Bahasan: cos2x = 1 2sin2x = 1 2()2 = 1 = http://meetabied.wordpress.com

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3. Diketahui tan p = maka cos 2p =. Bahasan: tan p = cos2p = 1 2sin2p = 1 2( )2 = 1 =125sin p = http://meetabied.wordpress.com

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4. Diketahui sudut lancip A dengan cos 2A = Nilai tan A = . Bahasan: cos 2A = 1 2sin2A = 1 2sin2A 2sin2A = 1 = http://meetabied.wordpress.com

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cos 2A = 2cos2A 1 = 2cos2A 1 2cos2A = + 1 = tan2A = = tan2A = A lancip Jadi, tan A = 2 http://meetabied.wordpress.com

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5. Diketahui A adalah sudut lancip dan cosA = Nilai sin A adalah. Bahasan: cos A = 2cos2A 1 = 2 - 1 = 2 - 1 = http://meetabied.wordpress.com

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cos x = 2 - 1cos x = cos x =

Jadi, nilai sin x = 1xx2 1http://meetabied.wordpress.com

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6. Buktikan: Bahasan: http://meetabied.wordpress.com

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Terbukti :http://meetabied.wordpress.com

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Rumus Sudut Rangkap tan 2a =

Contoh: 1. tan 20 = 2. tan 10x =http://meetabied.wordpress.com

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1. Jika tan A = 3 maka tan 2A =. Bahasan: tan 2A = = = = http://meetabied.wordpress.com

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2. Jika cos x = maka tan 2x =. Bahasan: tan 2x = = =51312http://meetabied.wordpress.com

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tan 2x = = =Jadi, tan 2x =http://meetabied.wordpress.com

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SELAMAT BELAJARhttp://meetabied.wordpress.com

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