Math  /  Trigonometry

QuestionGiven that cosθ=33,π2<θ<π\cos \theta=-\frac{\sqrt{3}}{3}, \frac{\pi}{2}<\theta<\pi, find the exact value of each of the following. (a) sin(2θ)\sin (2 \theta) (b) cos(2θ)\cos (2 \theta) (c) sinθ2\sin \frac{\theta}{2} (d) cosθ2\cos \frac{\theta}{2}

Studdy Solution
(a) sin(2θ)=223\sin(2\theta) = -\frac{2\sqrt{2}}{3} (b) cos(2θ)=13\cos(2\theta) = -\frac{1}{3} (c) sinθ2=3+36\sin\frac{\theta}{2} = \sqrt{\frac{3 + \sqrt{3}}{6}} (d) cosθ2=336\cos\frac{\theta}{2} = \sqrt{\frac{3 - \sqrt{3}}{6}}

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