Sinefull trigonometry

Geometry Level 3

Let \(\theta_{1} =\dfrac{2\pi}{3}\) , \(\theta_{2}=\dfrac{4\pi}{7}\), \(\theta_{3}=\dfrac{7\pi}{12}\). Then which of the following is true?

A. \((\sin \theta_1)^{\sin \theta_1} < (\sin \theta_2)^{\sin \theta_2} < (\sin \theta_3)^{\sin \theta_3}\)

B. \((\sin \theta_2)^{\sin \theta_2} < (\sin \theta_1)^{\sin \theta_1} < (\sin \theta_3)^{\sin \theta_3}\)

C. \((\sin \theta_3)^{\sin \theta_3} < (\sin \theta_1)^{\sin \theta_1} < (\sin \theta_2)^{\sin \theta_2}\)

D. \((\sin \theta_1)^{\sin \theta_1} < (\sin \theta_3)^{\sin \theta_3} < (\sin \theta_2)^{\sin \theta_2}\)

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