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Rumus jumlah dan selisih dua sudut sin( + ) = sin. cos + cos. sin( - ) = sin. cos - cos. sin http: //meetabied. wordpress. com

1. Sin 75 o = …. Bahasan: sin( + ) = sin. cos + cos. sin 750 = sin(450 + 300) = sin 450 cos 300 + cos 450 sin 300 = ½√ 2. ½√ 3 + ½√ 2. ½ = ¼√ 6 + ¼√ 2 = ¼√ 2(√ 2 + 1) http: //meetabied. wordpress. com

2. Diketahui sin A = cos B = A dan B adalah sudut-sudut lancip sin(A – B) =…. ? ? Bahasan: sin(A – B)= sin. Acos. B – cos. Asin. B 3 5 A 4 cos B = sin. A = cos. A = 24 7 25 B http: //meetabied. wordpress. com sin B =

sin A = cos A = cos B = sin B = sin(A – B) =…. = sin. Acos. B – cos. Asin. B = x - = = http: //meetabied. wordpress. com x

Rumus jumlah dan selisih dua sudut cos( + ) = cos - sin cos( - ) = cos + sin http: //meetabied. wordpress. com

1. Bahasan: cos + sin = cos( - ) = = = http: //meetabied. wordpress. com

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

= = 1 – tana. tanb jawab d http: //meetabied. wordpress. com

3. Tentukan nilai cos 56° + sin 56°. tan 28° Bahasan: cos 56° + sin 56°. tan 28° = cos 56° + sin 56°. = cos 56° + http: //meetabied. wordpress. com

= cos 56° + = =1 Jadi, Nilai cos 56° + sin 56°. tan 28° = 1 http: //meetabied. wordpress. com

4. Pada suatu segitiga siku-siku ABC berlaku cos. A. cos. B = ½. Maka cos(A – B) =…. Bahasan: siku-siku ABC; cos. A. cos. B = ½ maka ΔABC siku-siku di C C = 90° A + B + C = 180° A + B = 90° http: //meetabied. wordpress. com

A + B + C = 180° A + B = 90° A = 90° – B B = 90° – A cos(A – B) = cos. A. cos. B + sin. A. sin. B = ½ + sin(90 – B). sin(90 -A) = ½ + cos. B. cos. A =½+½ =1 Jadi cos(A – B) = 1 http: //meetabied. wordpress. com

Rumus jumlah dan selisih dua sudut tan( + ) = tan( - ) = http: //meetabied. wordpress. com

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

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

2. Diketahui A + B = 135° dan tan B = ½. Nilai tan A= …. Bahasan: A + B = 135° tan(A + B) = tan 135° = -1 http: //meetabied. wordpress. com

= -1 tan A + ½= -1 + ½tan A - ½tan A = -1 - ½ ½tan p = -1½ Jadi, tan p = -3 http: //meetabied. wordpress. com

3. Jika tan q = ½ dan p – q = ¼π maka tan p = …. Bahasan: p – q = ¼π tan(p – q) = tan ¼π =1 =1 http: //meetabied. wordpress. com

=1 tan p - ½ = 1 + ½tan p - ½tan p = 1 + ½ ½tan p = 1½ Jadi, tan p = 3 http: //meetabied. wordpress. com

Rumus Sudut Rangkap sin 2 a = 2 sina. cosa contoh: 1. sin 10° = 2 sin 5°. cos 5° 2. sin 6 P = 2 sin 3 P. cos 3 P 3. sin t = 2 sin½t. cos½t http: //meetabied. wordpress. com

1. Diketahui cos = Nilai sin 2 =…. Bahasan: cos = 5 4 sin = 3 http: //meetabied. wordpress. com

cos = 5 sin = 4 3 Jadi sin 2 = 2 sin. cos = 2. x = http: //meetabied. wordpress. com

2. Jika tan A = ½ maka sin 2 A =…. Bahasan: tan A = ½ sin. A = 1 2 A dan cos. A = sin 2 A = 2 sin. A. cos. A =2 x x = http: //meetabied. wordpress. com

3. Jika sinx – cosx = p maka harga sin 2 x =…. Bahasan: sinx – cosx = p (sinx – cosx)2 = p 2 sin 2 x – 2 sinx. cosx + cos 2 x = p 2 http: //meetabied. wordpress. com

sin 2 x – 2 sinx. cosx + cos 2 x = p 2 sin 2 x + cos 2 x – 2 sinx. cosx = p 2 1 – sin 2 x = p 2 1 – p 2 = sin 2 x Jadi, harga sin 2 x = 1 – p 2 http: //meetabied. wordpress. com

4. Diketahui A adalah sudut lancip dan cos½A = Nilai sin A = …. Bahasan: cos½A = t = √x - 1 √ 2 x ½A √x+ 1 dengan phytagoras t 2 = 2 x – (x + 1) t = √x - 1 http: //meetabied. wordpress. com

t = √x - 1 √ 2 x ½A √x+ 1 cos½A = sin½A = sin. A = 2 sin½A. cos½A =2 x = x Jadi, sin 2 x = http: //meetabied. wordpress. com

Rumus Sudut Rangkap cos 2 a = cos 2 a – sin 2 a = 2 cos 2 a – 1 = 1 – 2 sin 2 a http: //meetabied. wordpress. com

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

2. Diketahui sinx = ½ maka cos 2 x =…. Bahasan: cos 2 x = 1 – 2 sin 2 x = 1 – 2(½)2 =1–½ =½ http: //meetabied. wordpress. com

3. Diketahui tan p = ½ maka cos 2 p =…. Bahasan: tan p = ½ sin p = 1 2 √ 5 p cos 2 p = 1 – 2 sin 2 p = 1 – 2( )2 =1– = http: //meetabied. wordpress. com

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

• cos 2 A = 2 cos 2 A – 1 2 cos 2 A = tan 2 A = +1= 2 sin 2 A 2 cos 2 A = tan 2 A = ½ A lancip Jadi, tan A = ½√ 2 http: //meetabied. wordpress. com

5. Diketahui A adalah sudut lancip dan cos½A = Nilai sin A adalah…. Bahasan: cos A = 2 cos 2½A – 1 =2 =2 -1 -1 = http: //meetabied. wordpress. com

cos x = 2 -1 cos x = √x 2 x – 1 1 Jadi, nilai sin x = http: //meetabied. wordpress. com x

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

Terbukti : http: //meetabied. wordpress. com

Rumus Sudut Rangkap tan 2 a = Contoh: 1. tan 20° = 2. tan 10 x = http: //meetabied. wordpress. com

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

2. Jika cos x = maka tan 2 x =…. Bahasan: 13 12 tan 2 x = = x 5 = tan x = http: //meetabied. wordpress. com

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

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