Question

Tentukan himpunan penyelesaian persamaan trigonometri berikut untuk interval 0° < x < 360° : 2 sin² x - 5 sin x = -2

Answer 1

Given : trigonometri berikut  : 2 sin² x - 5 sin x = -2

To find : Tentukan himpunan penyelesaian persamaan untuk interval 0° < x < 360°

Solution:

2 sin² x - 5 sin x = -2

=> 2 sin² x - 5 sin x  +  2  = 0

=> 2 sin² x - 4 sin x - sinx   +  2  = 0

=> 2 Sinx  ( Sinx - 2) - 1 ( Sinx - 2) = 0

=> (2 Sinx - 1)(Sinx - 2) = 0

=> Sinx = 1/2  or  Sinx = 2    (

 Sinx = 2 ( not possible as    -1 ≤ Sinx ≤ 1 )

Sinx = 1/2  

=> x = 30°   , 150°

(30° , 150° )

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