SAT1000 - P322

Geometry Level pending

Given the function f(x)=sin2ωx2+12sinωx12 (ω>0)f(x)=\sin^2 \dfrac{\omega x}{2}+\dfrac{1}{2} \sin \omega x - \dfrac{1}{2}\ (\omega>0), xRx \in \mathbb R.

If f(x)=0f(x)=0 has no roots for x(π,2π)x \in (\pi, 2\pi), then find the range of ω\omega.

A. (0,18]A.\ (0,\dfrac{1}{8}]

B. (0,14][58,1]B.\ (0,\dfrac{1}{4}] \cup [\dfrac{5}{8},1]

C. (0,58]C.\ (0,\dfrac{5}{8}]

D. (0,18][14,58]D.\ (0,\dfrac{1}{8}] \cup [\dfrac{1}{4},\dfrac{5}{8}]


Have a look at my problem set: SAT 1000 problems

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