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Contents
Second Degree Equations
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Second Degree Equations This type of equations involves the square of the ratios, hence it is more complex to solve. This is where all the identities you have learnt will come in. Example 1
6 - 6 cos2x + cos x - 4 = 0 2 - 6 cos2 x + cos x = 0 (2 - 3 cos x)(1 + 2 cos x) = 0 basic angle = 60° or 48.19° x = 48.19°, 311.81°, 120° or 240°
Example 2
2 cosec x - 2 + 11 = 9 cosec x 2 cosec2 x - 9 cosec x + 9 = 0 (2 cosec x - 3)(cosec - 3) = 0 cosec x = 3/2 or 3 sin x = 2/3 or 1/3 basic angle = 41.81° or 19.41° x = 19.4°, 160.5°, 138.2° or 41.8°
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Solve for x between 0° and 360° for the equation 6 sin2 x = 6 - 6
cos2 x
6 sin2x = 6 - 6 cos2x (recall sin2
q
to cos2 q
= 1)
