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Solve the equation sin2 x + 3cos2 x = 0 for 0 ◦ ≤ x ≤ 360 ◦ .

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Solve the equation sin2 x + 3cos2 x = 0 for 0 ◦ ≤ x ≤ 360 ◦ .
asked May 4, 2013 in TRIGONOMETRY by andrew Scholar

1 Answer

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sin2x + 3cos2x = 0 for 0 ≤ x ≤ 2π

sin2x = -3cos2x

sin2x / cos2x = -3

Recall : Trigonometry identities tan2x = sin2x / cos2x

tan2x = -3

Recall : Trigonometry identities tan2x = 2tanx / (1 - tan2x)

2tanx / (1 - tan2x) = -3

2tanx = -3(1 - tan2x) = -3 + 3tan2x

3tan2x - 2tanx - 3 = 0

This is a quadratic equation for tanx

Substitute a = 3 , b = -2 and c = -3

There fore tanx = (- b ± √b2 - 4ac) / 2a

tanx = (2 ± √4 - 4(3)(-3) ) / 2(3) = (2 ±√4 + 36) / 6

tanx = (1 ± √10) / 3

x = tan-1[(1 ± √10) / 3].

 

 

answered May 4, 2013 by diane Scholar

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