Question
Solve for 0° ≤ θ ≤ 360°: 2 sin²θ + 3
sinθ − 2 = 0Solution
Let x = sinθ. 2x² + 3x − 2 = 0 Solve quadratic: Discriminant D = 3² − 4×2×(−2) = 9 + 16 = 25 x = [−3 ± 5]/(2×2) x₁ = (−3 + 5)/4 = 2/4 = 1/2 x₂ = (−3 − 5)/4 = −8/4 = −2 (not possible, since |sinθ| ≤ 1) So sinθ = 1/2 In [0°, 360°], sinθ = 1/2 at: θ = 30°, 150° Answer: θ = 30°, 150°.
Statement: F ≥ G > I > E ≤ P, E = S ≥ P
Conclusion: I. F ≥ P II. G > P
Statement: Y < Z > I < Q > S = M ≤ N
Conclusions:
I. S= N
II. Q > M
Statements: P = Q = R > S > T > Z; U > R < V < W > X
Conclusions:
I. W > Z
II. R < W
III. R < X
In the question, assuming the given statements to be true, find which of the conclusion (s) among given three conclusions is /are definitely true and ...
Statements: E < F > G; H < I ≤ F; E > D
Conclusions:
I. F > D
II. H < E
III. G < DWhich of the following will be definitely false if the given expression F > G ≥ H > I ≥ J > K = M ≤ N > L ≤ O is definitely true?
Statements: M @ N, P @ R, P & N
Conclusions: a ) M @ P b) R & M
...Statement: F < G; H ≥ I; H ≥ K; I > G ≥ J
Conclusion:
I. G > K
II. K > J
Statements: S = R, T ≤ U, O < J, T ≤ J, U > R
Conclusion:
I. R ≥ T
II. R < T
Statement: D < F; D ≥ E > G; I ≥ H > F
Conclusion:
I. G ≥ F
II. H ≥ D
