Questions: Find the exact value of tan^(-1)(1/sqrt(3)). a) -pi/3 b) pi/4 c) pi/3 d) pi/6

Solution Steps

To find the exact value of \(\tan^{-1}\left(\frac{1}{\sqrt{3}}\right)\), we need to determine the angle whose tangent is \(\frac{1}{\sqrt{3}}\). We can use known values of tangent for common angles to identify this. The angle that satisfies this condition is \(\frac{\pi}{6}\).

To find the exact value of \( \tan^{-1}\left(\frac{1}{\sqrt{3}}\right) \), we need to identify the angle \( \theta \) such that \( \tan(\theta) = \frac{1}{\sqrt{3}} \).

From trigonometric values, we know that: \[ \tan\left(\frac{\pi}{6}\right) = \frac{1}{\sqrt{3}} \] Thus, the angle \( \theta \) that satisfies \( \tan(\theta) = \frac{1}{\sqrt{3}} \) is \( \frac{\pi}{6} \).

Since \( \tan^{-1}\left(\frac{1}{\sqrt{3}}\right) = \frac{\pi}{6} \), we can confirm that this corresponds to option d) in the multiple-choice question.

Final Answer