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Solve the trigonometric equation 2cos^2(x)+3sin(x)=0

Solve the trigonometric equation 2cos^2(x)+3sin(x)=0

Grade:11

2 Answers

Arun
25750 Points
5 years ago
Dear student
 
I have attached image containing solution in case of any difficulty please feel free to ask.
 
Arun
25750 Points
5 years ago
replace cos^2 with 1-sin^2 x 

2(1-sin^x) + 3sinx = 0 
-2sin^2x + 3sinx + 2 = 0 

2sin^2x -3sinx - 2 = 0 
(2sinx + 1)(sinx - 2) = 0 
sinx = -1/2 or sinx =2 ---but sinx cannot = 2 so just work with -1/2 

sinx = -1/2 quadrants III and IV 
x = 210 deg (or 7pi/6) + 2npi in QIII 
x = 330 deg (or 11pi/6) + 2npi in QIV

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