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Trig General solution question help?
Whats the general solution for 5sinx-3cosx+2=0. plz show all steps not just the answer
1 Answer
- EMLv 78 years agoFavorite Answer
5 sin x + 2 = 3 cos x
25 sin²x + 20 sin x + 4 = 9 cos²x
25 sin²x + 20 sin x + 4 + 9 sin²x = 9 cos²x + 9 sin²x
34 sin²x + 20 sin x + 4 = 9
34 sin²x + 20 sin x - 5 = 0
sin x = [-20 ± sqrt{20² - 4(34)(-5)}] / [2(34)]
sin x = [-20 ± sqrt{1080}] / [2(34)]
sin x = [-10 ± 3 sqrt(30)] / 34
Possible solutions on -180° ≤ x < 180°:
x = arcsin{[-10 + 3 sqrt(30)] / 34} ≈ 10.90°
x ≈ 180 - 10.90° = 169.10°
x = arcsin{[-10 - 3 sqrt(30)] / 34} ≈ -51.02°
x ≈ -180 - (-51.02°) = -128.98°
Check each of these in the original equation and you'll find that only the solutions in quadrants I and III satisfy it.
x = 10.90° + 360°n or
x = -128.98° + 360°n
