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RUMUS JUMLAH DAN SELISIH SUDUT

P 3 (cos (a+b), sin (a+b)). P 2 (cos b, sin b). P 1 (cos a, sin a). RUMUS JUMLAH DAN SELISIH SUDUT. Q (1, 0). P 4 (cos a, -sin a). Busur QP 1 = a Busur QP 2 = b Busur P 4 Q = = a Busur P 2 P 3 = a. Busur QP 3 = Busur QP 2 + Busur P 2 P 3 = b + a

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RUMUS JUMLAH DAN SELISIH SUDUT

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  1. P3 (cos (a+b), sin (a+b)) P2 (cos b, sin b) P1 (cos a, sin a) RUMUS JUMLAH DAN SELISIH SUDUT Q (1, 0) P4 (cos a, -sin a)

  2. Busur QP1 = a • Busur QP2 = b • Busur P4Q = = a • Busur P2P3 = a • Busur QP3 = Busur QP2 + Busur P2P3 • = b + a • Busur P4P2 = Busur P4Q + Busur QP2 • = a + b • Tali Busur P2P4 = Tali Busur QP3 • Rumus Jarak Dua titik pada Koordinat Kartesius • Shg P3 (cos (a+b), sin (a+b)) P2 (cos b, sin b) P1 (cos a, sin a) Q (1, 0) P4 (cos a, -sin a) Shg :

  3. Dari Ruas Kiri (Ri) • (cos b – cos a)2 + (sin b + sin a)2 • cos2 b – 2 cos a.cos b + cos2 a + sin2 b + 2 sin a. sin b + sin2 a • cos2 b + sin2 b + cos2 a + sin2 a – 2 cos a. cos b + 2 sin a. sin b • 1 + 1 – 2 (cos a. cos b – sin a. sin b) • 2 – 2 (cos a. cos b – sin a. sin b) • Dari Ruas Kanan (Ra) • cos2 (a+b) – 2 cos (a+b) + 1 + sin2 (a+b) • cos2 (a+b) + sin2 (a+b)– 2 cos (a+b) + 1 • 1 - 2 cos (a+b) + 1 • 2 - 2 cos (a+b) Sehingga didapatkan : 2 - 2 cos (a+b) = 2 – 2 (cos a. cos b – sin a. sin b) Kesimpulan : cos (a + b) = cos a. cos b – sin a. sin b

  4. cos (a + b) = cos a. cos b – sin a. sin b cos (a – b) = cos (a + (-b)) = cos a cos (-b) – sin a sin (-b) = cos a cos b + sin a sin b Sehingga : cos (a – b) = cos a cos b + sin a sin b Diketahui : dan Sin (a + b) = = = = Diperoleh : Sin (a + b) = sin a cos b + cos a sin b

  5. Bagaimana dengan Sin (a – b) = ? Sin (a – b) = sin (a + (-b)) sin a.cos (-b) + cos a. sin (-b) sin a. cos b – cos a. sin b Sin (a – b) = sin a. cos b – cos a. sin b Juga

  6. rumus jumlah dan selisih dua sudut sin (a + b) = sin a cos b + cos a sin b sin (a – b) = sin a. cos b – cos a. sin b cos (a + b) = cos a. cos b – sin a. sin b cos (a – b) = cos a cos b + sin a sin b

  7. Contoh soal Tanpa menggunakan tabel/kalkulator, hitunglah nilai dari : • Sin 75o Jawab.

  8. Latihan Tanpa Menggunakan Tabel/kalkulator, tentukan nilai dari • Sin 110o • Cos 15o • Tan 345o Jika sin a = dan sin b = Dengan a dan b sudut lancip Tentukan • Cos (a + b) • Cos (a – b)

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