Mathematics

Mathematics

Problem

If 90∘<x<180∘90^{\circ}<x<180^{\circ}, which of the following statements about sin⁡2x\sin 2x is correct? a) sin⁡2x\sin 2x is positive because 2x2x remains in the second quadrant where sine is positive. b) sin⁡2x\sin 2x is negative because sin⁡x\sin x is positive and cos⁡x\cos x is negative. c) sin⁡2x\sin 2x is positive since sin⁡2x=2sin⁡2x\sin 2x = 2\sin^{2}x and sin⁡x\sin x is positive. d) sin⁡2x\sin 2x is zero because 2x=180∘2x=180^{\circ} when xx is the midpoint of the interval.

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