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Himpunan penyelesaian dari persamaan trigonometri cos 2 2 x = 1 − sin 2 x pada interval 0 ≤ x ≤ 18 0 o adalah ….

Himpunan penyelesaian dari persamaan trigonometri  pada interval  adalah ….

  1. begin mathsize 14px style open curly brackets 30 to the power of straight o comma straight 45 to the power of straight o comma straight 145 to the power of straight o close curly brackets end style 

  2. begin mathsize 14px style open curly brackets 35 to the power of straight o comma straight 65 to the power of straight o comma straight 145 to the power of straight o close curly brackets end style 

  3. begin mathsize 14px style open curly brackets 0 to the power of straight o comma straight 45 to the power of straight o comma straight 85 to the power of straight o comma straight 155 to the power of straight o close curly brackets end style 

  4. begin mathsize 14px style open curly brackets 0 to the power of straight o comma straight 30 to the power of straight o comma straight 90 to the power of straight o comma straight 180 to the power of straight o close curly brackets end style 

  5. begin mathsize 14px style open curly brackets 0 to the power of straight o comma straight 45 to the power of straight o comma straight 90 to the power of straight o comma straight 180 to the power of straight o close curly brackets end style 

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M. Robo

Master Teacher

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himpunan penyelesaiannya .

himpunan penyelesaiannya begin mathsize 14px style open curly brackets 0 to the power of straight o comma straight 45 to the power of straight o comma straight 90 to the power of straight o comma straight 180 to the power of straight o close curly brackets end style . 

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Sehingga diperoleh, (i) Penyelesaian: Untuk k = 0 maka Untuk k = 1 maka Untuk k = 0 maka (ii) Penyelesaian: Untuk k = 0 maka Jadi himpunan penyelesaiannya .

Error converting from MathML to accessible text.   

Sehingga diperoleh,

(i) begin mathsize 14px style sin space 2 straight x equals 0 equals sin space 0 to the power of straight o end style 

Penyelesaian:

begin mathsize 14px style 2 straight x equals 0 to the power of straight o plus 360 to the power of straight o straight k straight x equals 0 to the power of straight o plus 180 to the power of straight o straight k end style 

Untuk k = 0 maka begin mathsize 14px style straight x equals 0 degree end style 

Untuk k = 1 maka begin mathsize 14px style straight x equals 180 degree end style 

begin mathsize 14px style 2 straight x equals 180 to the power of straight o plus 360 to the power of straight o straight k straight x equals 90 to the power of straight o plus 180 to the power of straight o straight k end style 

Untuk k = 0 maka begin mathsize 14px style straight x equals 90 degree end style 

 

(ii) begin mathsize 14px style sin space 2 straight x equals 1 equals sin space 90 to the power of straight o end style 

Penyelesaian:

begin mathsize 14px style 2 straight x equals 90 to the power of straight o plus 360 to the power of straight o straight k straight x equals 45 to the power of straight o plus 180 to the power of straight o straight k end style 

Untuk k = 0 maka begin mathsize 14px style straight x equals 45 degree end style 

Jadi himpunan penyelesaiannya begin mathsize 14px style open curly brackets 0 to the power of straight o comma straight 45 to the power of straight o comma straight 90 to the power of straight o comma straight 180 to the power of straight o close curly brackets end style . 

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