Trigonometry #1

Geometry Level 2

Find the sum of all θ \theta between 0 ∘ 0^{\circ} and 36 0 ∘ 360^{\circ} such that

sin ⁡ θ = − 1 2 . \sin\theta=-\frac{1}{2}.


The answer is 540.

Victor Loh by Victor Loh , 19, Singapore

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2 solutions

Akshay Sant
Jul 12, 2014

since sin is only negative in 3rd and 4 th quadrant thus Knowing θ \theta = 210° and 330° Thus .. adding Sum = 540°

Thats it..... !!

3 Helpful 0 Interesting 0 Brilliant 0 Confused

sin θ = sin (180'+30') & sinθ = (360-30) so, θ = 210 , 330 so ans is 210+330=540

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