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Trigonometric Equations

General Solution of Simple Trigonometric Equations

Which of the following is the general solution of $2\sqrt{3}=4\sin x?$

x=2n\pi+\frac{\pi}{3}

x=2n\pi+\frac{2}{3}\pi

x=2n\pi\pm\frac{\pi}{3}

x=2n\pi+\frac{\pi}{6}

x=2n\pi+\frac{5}{6}\pi

x=2n\pi\pm\frac{\pi}{6}

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by Brilliant Staff

Which of the following is the general solution for the equation $\frac{\sqrt{3}}{3}=\tan4x?$

{4}n\pi +\frac{\pi}{3}

{4}n\pi +\frac{\pi}{6}

\frac{n}{4}\pi +\frac{\pi}{12}

\frac{n}{4}\pi +\frac{\pi}{24}

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by Brilliant Staff

Which of the following is the general solution for the equation $\sqrt{3}=2\sin(12x+\frac{3}{11}\pi)?$

x=2n\pi+\frac{1}{3}\pi

x=2n\pi+\frac{2}{3}\pi

x=2n\pi+\frac{2}{33}\pi

x=2n\pi+\frac{13}{33}\pi

x=\frac{n}{6}\pi+\frac{1}{198}\pi

x=\frac{n}{6}\pi+\frac{13}{396}\pi

x=\frac{n}{6}\pi+\frac{1}{3}\pi

x=\frac{n}{6}\pi+\frac{1}{2}\pi

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by Brilliant Staff

What is the general solution for the equation $8\cos150^\circ=4\tan\left(7x+\frac{3}{7}\pi\right)?$

x=\left(\frac{2n}{7}\pm\frac{5}{49}\right)\pi

x=\left(\frac{n}{7}+\frac{5}{147}\right)\pi

x=\left(\frac{n}{7}+\frac{5}{49}\right)\pi

x=\left(\frac{2n}{7}\pm\frac{5}{147}\right)\pi

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by Brilliant Staff

Which of the following is a general solution of the equation $\tan \left(x+\frac{37}{3}\pi \right) = 1 ?$

n\pi+\frac{3\pi}{4}

n\pi-\frac{3\pi}{4}

n\pi-\frac{\pi}{12}

n\pi+\frac{\pi}{12}

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by Brilliant Staff