RUMUS-RUMUS TRIGONOMETRI, RUMUS JUMLAH DAN PENGURANGAN COSINUS 1 (Sukino, 2007: 150 -151)

RUMUS-RUMUS TRIGONOMETRI

RUMUS JUMLAH DAN PENGURANGAN COSINUS

(Sukino, 2007: 150 - 151)

Rumus:

1. cos (A + B) = cos A. cos B – sin A. sin B

2. cos (A - B) = cos A. cos B + sin A. sin B

Latihan Kompetensi Siswa 1

1. cos (x + 30°) = …

Jawab:

cos (x + 30°) = cos x. cos 30° - sin x. sin 30°

                       = cos x. 1/2√3 – sin x. ½

                       = ½(√3 cos x – sin x) …C

2. cox (x- 45°) = …..

Jawab:

cos (x - 45°)     = cos x. cos 45° + sin x. sin 45°

                        = cos x. 1/2√2 + sin x 1/2 √2

                        = ½ √2 (cos x + sin x) …A

3. cos 75° = …

Jawab:

Cos 75°     = cos (30 + 45) °

                  = cos 30°. cos 45° - sin 30°. Sin 45°

                  = ½ √3 . ½ √2 – ½ . ½ √2

                  = ¼ √2 (√3 -1) …A

4. cos 15° = …

Jawab:

Cos 15°     =  cos (45-30) °

                  = cos 45°. cos 30° + sin 45° . sin 30°

                  = ½ √2. ½ √3 + ½ √2 . ½

                  = ¼ √2 (√3 + 1) . √2/√2

                  = 2/4√2 (√3 +1)

                  = (√3 + 1)/2√2  … A

5. cos (x + y) cos (x – y) = …

Jawab:

Cos (x + y) cos (x – y) = cos ½(2x + 2y) cos ½ (2x – 2y)

                                      = ½ (cos 2x + cos 2y)

                                      = ½ (2 cos²x -1 + 2 cos²y -1)

                                      = ½ (2 cos²x + 2cos²y – 2)

                                      = cos² x + cos²y – 1

                                      = cos² x + cos²y – (sin²y + cos²y)

                                      = cos² x - sin²y … C