Question

tolong bantu no 7 dongg

Answer 1

Jawaban:

e. {7π/6 , 11π/6}

Penjelasan dengan langkah-langkah:

Trigonometri

sifat trigonometri :

• cos 2x = 1-2sin²x

cos 2x + 5 sin x + 2 = 0

1-2sin²x + 5 sin x + 2 = 0

1 + 2 - 2sin²x + 5 sin x = 0

3 - 2sin²x + 5 sin x = 0

.... sin x = u

3 - 2u² + 5u = 0

2u² - 5u - 3 = 0

2u² + 1u - 6u -3 = 0

u(2u+1) -3(2u+1) = 0

(2u+1) (u-3) = 0

diperoleh

2u + 1 = 0

u = -½

dan

u + 3 = 0

u = -3

sehingga

sin x = -½

x = 7π/6

dan

sin x = -3

x = 11π/6

maka x { 7π/6 , 11π/6 } (e) ✓