5
5. TRIGONOMETRI II
A. Jumlah dan Selisih Dua Sudut
1) sin (A ( B) = sin A cos B ( cos A sin B
2) cos (A ( B) = cos A cos B [pic] sin A sin B
3) tan (A ( B) = [pic]
B. Perkalian Sinus dan Kosinus
1) 2sin A cos B = sin(A + B) + sin(A – B)
sin A cos B = ½{sin(A + B) + sin(A – B)}
2) 2cos A sin B = sin(A + B) – sin(A – B)
cos A sin B = ½{sin(A + B) – sin(A – B)}
3) 2cos A cos B = cos(A + B) + cos(A – B)
cos A cos B = ½{cos(A + B) + cos(A – B)}
4) –2sin A sin B = cos(A + B) – cos(A – B)
sin A sin B = –½{cos(A + B) – cos(A – B)}
C. Penjumlahan dan Pengurangan Sinus, Kosinus dan Tangen
1) sin A + sin B = 2sin ½ (A + B) · cos ½(A – B)
2) sin A – sin B = 2cos½ (A + B) · sin ½(A – B)
3) cos A + cos B = 2cos½ (A + B) · cos ½(A – B)
4) cos A – cos B = –2sin½ (A + B) · sin½(A – B)
5) tan A + tan B = [pic]
6) tan A – tan B = [pic]
D. Sudut Rangkap
1) sin 2A = 2sinA·cosA
2) cos 2A = cos2A – sin2A
= 2cos2A – 1
= 1 – 2sin2A
3) tan 2A = [pic]
4) Sin 3A = 3sin A – 4sin3A
E. Persamaan Trigonometri
1. sin xº = sin p
x1 = p + 360k
x2 = (180 – p) + 360k
2. cos xº = cos p
x1 = p + 360k
x2 = – p + 360k
3. tan xº = tan p
x1 = p + 180k
x2 = (180 + p) + 180k
4. Bentuk: A trig2 + B trig + C = 0 diselesaikan seperti menyelesaikan persamaan kuadrat
|SOAL |PENYELESAIAN |
|UN 2004 | |
|Nilai sin 45º cos 15º + cos 45º sin 15º sama dengan … | |
|A. [pic] D. [pic][pic] | |
|B. [pic][pic] E. [pic][pic] | |
|C. [pic][pic] | |
| | |
|UN 2012/D49 | |
|Diketahui nilai sin ( cos ( = [pic] dan sin (( – ( ) = [pic] untuk | |
|0( ( ( ( 180( dan | |
|0( ( ( ( 90(. Nilai sin (( + ( ) = …. | |
|A. – [pic] D. [pic] | |
|B. – [pic] E. [pic] | |
|C. – [pic] | |
| | |
|UN 2012/E52 | |
|Diketahui sin ( = [pic] dan cos ( = [pic] (( dan ( sudut lancip). | |
|Nilai sin(( + ()=…. | |
|A. [pic] D. [pic] | |
|B. [pic] E. [pic] | |
|C. [pic] | |
| | |
| | |
|UN 2012/C37 | |
|Diketahui [pic] dan sin ( sin ( = [pic] dengan ( dan ( merupakan | |
|sudut lancip. Nilai cos (( + () = … | |
|1 | |
|[pic] | |
|[pic] | |
|[pic] | |
|0 | |
| | |
| | |
|UN 2012/B25 | |
|Jika A + B = [pic] dan cos A cos B = [pic], maka cos(A – B) = ... | |
|A. [pic] D. 1 | |
| | |
|B. [pic] E. [pic] | |
| | |
|C. [pic] | |
| | |
| | |
|UN 2011 PAKET 12 | |
|Diketahui (A + B) = [pic] dan sinA sinB = [pic]. Nilai dari cos (A –| |
|B) = … | |
|A. –1 D. [pic] | |
|B. –[pic] E. 1 | |
|C. [pic] | |
|UN 2008 PAKET A/B | |
|Diketahui sin A = [pic] dan sin B = [pic], dengan A sudut lancip dan| |
|B sudut tumpul. | |
|Nilai cos (A – B) = … | |
|[pic] | |
|[pic] | |
|[pic] | |
|[pic] | |
|[pic] | |
| | |
|UN 2010 PAKET B | |
|Diketahui p dan q adalah sudut lancip dan | |
|p – q = 30(. Jika cos p sin q = [pic], maka nilai dari sin p cos q =| |
|… | |
|A. [pic] D. [pic] | |
|B. [pic] E. [pic] | |
|C. [pic] | |
| | |
|UN 2009 PAKET A/B | |
|Pada segitiga ABC lancip, diketahui cos A = [pic] dan sin B = [pic],| |
|maka sin C = … | |
|A. [pic] D. [pic] | |
|B. [pic] E. [pic] | |
|C. [pic] | |
|UAN 2003 | |
|Nilai dari [pic]adalah … | |
|3 | |
|2 | |
|1 | |
|[pic] | |
|[pic] | |
| | |
| | |
|UN 2012/C37 | |
|Nilai dari sin 75(– sin 165( adalah … | |
|A. [pic] D. [pic] | |
|B. [pic] E. [pic] | |
|C. [pic] | |
| | |
| | |
|UN 2008 PAKET A/B | |
|Nilai dari cos 195º + cos 105º adalah … | |
|[pic] | |
|[pic] | |
|[pic] | |
|0 | |
|[pic] | |
| | |
| | |
|UN 2007 PAKET B | |
|Nilai dari cos 25º + cos 95º + cos 145º = …. | |
|–1 | |
|– [pic] | |
|0 | |
|[pic] | |
|1 | |
| | |
| | |
|UN 2006 | |
|Nilai dari sin 75º + cos 75º = … | |
|[pic][pic] | |
|[pic][pic] | |
|[pic][pic] | |
|1 | |
|[pic][pic] | |
| | |
| | |
| | |
|UAN 2003 | |
|Nilai [pic] = … . | |
|[pic] | |
|[pic][pic] | |
|[pic][pic] | |
|–[pic][pic] | |
|–[pic] | |
| | |
|UN 2011 PAKET 12 | |
|Nilai [pic] = … | |
|a. –[pic] | |
|b. –[pic] | |
|c. –[pic] | |
|d. [pic] | |
|e. [pic] | |
| | |
|UN 2011 PAKET 46 | |
|Nilai [pic] = … | |
|a. –[pic] | |
|b. –[pic] | |
|c. –1 | |
|d. [pic] | |
|e. 1 | |
|UN 2010 PAKET A | |
|Hasil dari [pic]= … | |
|–[pic] | |
|– [pic][pic] | |
|1 | |
|[pic][pic] | |
|[pic] | |
| | |
|UN 2007 PAKET A | |
|Nilai dari [pic]= …. | |
|– [pic] | |
|–[pic] | |
|[pic][pic] | |
|[pic] | |
|[pic] | |
|UN 2010 PAKET B | |
|Hasil dari [pic]= … | |
|–[pic] | |
|1 | |
|[pic][pic] | |
|1 | |
|[pic] | |
|UN 2010 PAKET A | |
|Diketahui tan ( – tan ( = [pic] dan | |
|cos ( cos ( = [pic], (( , ( lancip). | |
|Nilai sin (( – () = … | |
|A. [pic] D. [pic] | |
|B. [pic] E. [pic] | |
|C. [pic] | |
|UAN 2003 | |
|Diketahui A sudut lancip dengan cos 2A = [pic]. Nilai tan A = … | |
|[pic] | |
|[pic] | |
|[pic] | |
|[pic] | |
|[pic] | |
|UN 2012/C37 | |
|Himpunan penyelesaian persamaan | |
|cos 2x – 2cos x = –1; 0 ( x ( 2( adalah … | |
|{0, [pic](, [pic](, 2(} | |
|{0, [pic](, [pic](, 2(} | |
|{0, [pic](, (, [pic]} | |
|{0, [pic](, [pic](} | |
|{0, [pic](, (} | |
|UN 2011 PAKET 46 | |
|Himpunan penyelesaian persamaan | |
|cos 2x – 3 cos x + 2 = 0, 0( ( x ( 360( adalah … | |
|a. {60(, 300(} | |
|b. {0(, 60(, 300(} | |
|c. {0(, 60(, 180(, 360(} | |
|d. {0(, 60(, 300(, 360(} | |
|e. {0(, 60(, 120(, 360(} | |
|UN 2011 PAKET 12 | |
|Himpunan penyelesaian persamaan | |
|cos 2x + cos x = 0, 0( ( x ( 180( adalah … | |
|a. {45(, 120(} | |
|b. {45(, 135(} | |
|c. {60(, 135(} | |
|d. {60(, 120(} | |
|e. {60(, 180(} | |
| | |
|UN 2005 | |
|Himpunan penyelesaian dari persamaan | |
|cos 2xº + 3 sin xº = 2, untuk 0 ( x ( 360 adalah … | |
|{30, 90} | |
|{30, 150} | |
|{0, 30, 90} | |
|{30, 90, 150} | |
|{30, 90, 150, 180} | |
| | |
|UN 2008 PAKET A/B | |
|Himpunan penyelesaian persamaan: | |
|cos 2x( + 7 sin x( + 3 = 0, untuk 0 < x < 360 adalah … | |
|a. {0, 90} | |
|b. {90, 270} | |
|c. {30, 130} | |
|d. {210, 330} | |
|e. {180, 360} | |
| | |
|UN 2012/D49 | |
|Himpunan penyelesaian dari persamaan | |
|cos 4x + 3 sin 2x = – 1 untuk 0( ( x ( 180( adalah …. | |
|A.{120(,150(} | |
|B. {105(,165(} | |
|C. {30(,150(} | |
|D. {30(,165(} | |
|E. {15(,105(} | |
| | |
| | |
|UN 2012/A13 | |
|Himpunan penyelesaian persamaan | |
|cos 2x – 2sin x = 1; 0 ( x < 2( adalah…. | |
|{0,[pic]} | |
|{0,[pic]} | |
|{0,[pic]} | |
|{0,[pic]} | |
|{0,[pic]} | |
| | |
| | |
|UN 2010 PAKET B | |
|Himpunan penyelesaian persamaan: | |
|cos 2x – sin x = 0, untuk 0 ( x ( 2( adalah … | |
|a. [pic] | |
|b. [pic] | |
|c. [pic] | |
|d. [pic] | |
|e. [pic] | |
|UN 2010 PAKET A | |
|Himpunan penyelesaian persamaan: | |
|sin 2x + 2cos x = 0, untuk 0 ( x < 2( adalah … | |
|A. [pic] D. [pic] | |
|B. [pic] E. [pic] | |
|C. [pic] | |
| | |
| | |
|UN 2009 PAKET A/B | |
|Himpunan penyelesaian persamaan: | |
|sin 4x – cos 2x = 0, untuk 0( < x < 360( adalah … | |
|a. {15(, 45(, 75(, 135(} | |
|b. {135(, 195(, 225(, 255(} | |
|c. {15(, 45(, 195(, 225(} | |
|d. {15(, 75(, 195(, 255(} | |
|e. {15(, 45(, 75(, 135(, 195(,225(, 255(,315(} | |
|UN 2004 | |
|Nilai x yang memenuhi persamaan | |
|2 cos xº + 2sin xº = [pic]untuk 0 ( x ( 360 adalah … | |
|15 atau 135 | |
|45 atau 315 | |
|75 atau 375 | |
|105 atau 345 | |
|165 atau 285 | |
|UN 2006 | |
|Diketahui persamaan | |
|2cos2x + [pic]sin 2x = 1 + [pic], untuk | |
|0 < x < [pic]. Nilai x yang memenuhi adalah … | |
|[pic]dan[pic] | |
|[pic]dan[pic] | |
|[pic]dan[pic] | |
|[pic]dan[pic] | |
|[pic]dan[pic] | |
| | |
|UN 2004 | |
|Nilai x yang memenuhi | |
|[pic]cos x + sin x =[pic], untuk 0 ( x ( 2( adalah … | |
|a. [pic] dan [pic] d. [pic] dan [pic] | |
| | |
|b. [pic] dan [pic] e. [pic] dan [pic] | |
| | |
|c. [pic] dan [pic] | |
| | |
|UAN 2003 | |
|Untuk 0 ( x ( 360, himpunan penyelesaian dari sin xº –[pic]cos xº | |
|–[pic] = 0 adalah … | |
|{120,180} | |
|{90,210 | |
|{30, 270} | |
|{0,300} | |
|{0,300,360} | |
|EBTANAS 2002 | |
|Jika a sin xº + b cos xº = sin(30 + x)º untuk setiap x, maka a[pic]+| |
|b = … | |
|–1 | |
|–2 | |
|1 | |
|2 | |
|3 | |
| | |
| | |
|SOAL |PENYELESAIAN |
| | |
| | |
| | |
| | |
| | |
| | |
| | |
| | |
| | |
| | |
| | |
| | |
| | |
| | |
| | |
................
................
In order to avoid copyright disputes, this page is only a partial summary.
To fulfill the demand for quickly locating and searching documents.
It is intelligent file search solution for home and business.