Trigonometry

Geometry Level 2

If sin ⁡ θ = 3 2 \sin{\theta}=\dfrac{\sqrt{3}}{2} for 0 < θ < π 2 0<\theta<\dfrac{\pi}{2} evaluate sin ⁡ ( θ 2 ) \sin\left({\dfrac{\theta}{2}}\right) .


The answer is 0.5.

Akeel Howell by Akeel Howell , 22, USA

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1 solution

Nikhil Raj
Jun 7, 2017

sin ⁡ θ = 3 2 θ = sin ⁡ − 1 3 2 = 60 θ 2 = 30 S o , sin ⁡ 30 = 1 2 \sin \theta = \dfrac{\sqrt{3}}{2} \\ \theta = \sin^{-1}\dfrac{\sqrt{3}}2 = 60 \\ \dfrac{\theta}{2} = 30 \\ So, \sin 30 =\huge \boxed{\dfrac{1}{2}}

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