Tentukan himpunan penyelesaian dibawah ini untuk 0° ≤ x ≤ 360"

a 2 sin 2 x = √3 b. cos 2x ½/2

C. sin x = 1/2√3

d. sin (60" + x) -sin (60°-x) = 1

e. sin 5x-sin x = 0

Tentukan himpunan penyelesaian dibawah ini untuk 0° ≤ x ≤ 360″

Jawab :

0° ≤ x ≤ 360°

a. 2 sin (2x) = $sqrt{3}$

sin 2x = $frac{1}{2}sqrt{3}$

1. sin 2x = sin 60°

2x = 60°

x = 30°

2. sin 2x = sin 120°

2x = 120°

x = 60°

3. sin 2x = sin 420°

2x = 420°

x = 210°

4. sin 2x = sin 480°

2x = 480°

x = 240°

Hp = {30°, 60°, 210°, 240°}

b. cos 2x = $frac{1}{2}sqrt{2}$

1. cos 2x = cos 45°

2x = 45°

x = 22,5°

2. cos 2x = cos 315°

2x = 315°

x = 157,5°

3. cos 2x = cos 405°

2x = 405°

x = 202,5°

4. cos 2x = cos 675°

2x = 675°

x = 337,5°

Hp = {22,5°, 157,5°, 202,5°, 337,5°}

c. sin x = $frac{1}{2}sqrt{3}$

1. sin x = sin 60°

x = 60°

2. sin x = sin 120°

x = 120°

Hp = {60°, 120°}

d. sin (60+x)° – sin (60-x)° = 1

2 cos 60° sin x = 1

2 × $frac {1}{2}$ sin x = 1

sin x = 1

sin x = sin 90°

x = 90°

Hp = {90°}

e. sin 5x – sin x = 0

2 cos 3x sin 2x = 0

cos 3x sin 2x = 0

I. cos 3x = 0

1. cos 3x = cos 90°

3x = 90°

x = 30°

2. cos 3x = cos 270°

3x = 270°

x = 90°

3. cos 3x = cos 450°

3x = 450°

x = 150°

4. cos 3x = cos 630°

3x = 630°

x = 210°

5. cos 3x = cos 810°

3x = 810°

x = 270°

6. cos 3x = cos 990°

3x = 990°

x = 330°

II. sin 2x = 0

1. sin 2x = sin 0°

2x = 0°

x = 0°

2. sin 2x = sin 180°

2x = 180°

x = 90°

3. sin 2x = sin 360°

2x = 360°

x = 180°

4. sin 2x = sin 540°

2x = 540°

x = 270°

5. sin 2x = sin 720°

2x = 720°

x = 360°

Hp = {0°, 30°, 90°, 150°, 180°, 210°, 270°, 330°, 360°}