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(150^\circ) was incorrectly written as ( \frac{2\pi}{3} ) radians. What is the correct radian form?

Answer and explanation

Correct answer: ( \frac{5\pi}{6} ) radians

To convert degrees into radians, use the fact that \(180^\circ=\pi\) radians. Therefore an angle measured in degrees is multiplied by \(\frac{\pi}{180}\). For this angle, \(150^\circ\times\frac{\pi}{180}=\frac{150\pi}{180}=\frac{5\pi}{6}\), after cancelling the common factor 30. Hence the correct choice is B.

The proposed expression \(\frac{2\pi}{3}\) is not equal to 150 degrees. Converting it back gives \(\frac{2\pi}{3}\times\frac{180^\circ}{\pi}=120^\circ\). This identifies why it is incorrect. The other choices represent different angles: \(\frac{3\pi}{4}\) is 135 degrees, while \(\frac{7\pi}{6}\) and \(\frac{4\pi}{3}\) are larger than 180 degrees.

Related tags

Trigonometric-FunctionsAnglesError-Correction

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