Solve the trigonometric equation 2cos^2(x)+3sin(x)=0
Nipun rajeev , 7 Years ago
Grade 11
Trigonometry> Solve the trigonometric equation 2cos^2(x...
2 Answers
Arun
Dear student
I have attached image containing solution in case of any difficulty please feel free to ask.
Arun
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
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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