JEE MATHEMATICS MCQ: TRIGONOMETRIC EQUATIONS

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Analyzing +4 | -1

The sum of the series

\sum\limits_{n = 1}^\infty {\sin \left( {\frac{{n!\,\,\pi }}{{720}}} \right)}

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Correct option: C

\sin \left(\frac{\pi}{6}\right)+\sin \left(\frac{\pi}{30}\right)+\sin \left(\frac{\pi}{120}\right)+\sin \left(\frac{\pi}{360}\right)+\sin \left(\frac{\pi}{720}\right)

Option C (

\sin \left(\frac{\pi}{6}\right)+\sin \left(\frac{\pi}{30}\right)+\sin \left(\frac{\pi}{120}\right)+\sin \left(\frac{\pi}{360}\right)+\sin \left(\frac{\pi}{720}\right)

) is correct because after the first five terms, all subsequent terms become multiples of

\pi

and thus their sine values are zero.

More Questions from TRIGONOMETRIC EQUATIONS

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\left[ {0,\;\,\frac{\pi }{2}} \right]

\left( {x,\,y} \right)

x,\,\,y \in \left[ {0,10} \right]

\left( {\sqrt {{{\sin }^2} - \sin \,\,x + \frac{1}{2}} } \right){2^{{{\sec }^2}y}}\,\, \cdot \,\, \le 1

\mathrm{X}

\theta \rightarrow \frac{\pi}{2}

\sin x+\cos x=\frac{\sqrt{7}}{2}

x \in\left[0, \frac{\pi}{4}\right]

\tan \frac{x}{2}

\tan \frac{\pi}{5}+2 \tan \frac{2 \pi}{5}+4 \cot \frac{4 \pi}{5}

0 < x < \pi

\cos x+\sin x=\frac{1}{2}

\tan x