Questions: Find the exact value of the expression 6 cos (π/6) - 3 tan (π/4) Select the correct choice below and, if n A. 6 cos (π/6) - 3 tan (π/4) = □ (Simplify your answer. Type an ex B. The answer is undefined.

Solution Steps

To solve the expression \(6 \cos \frac{\pi}{6} - 3 \tan \frac{\pi}{4}\), we need to evaluate the trigonometric functions at the given angles. The cosine of \(\frac{\pi}{6}\) and the tangent of \(\frac{\pi}{4}\) are well-known values from the unit circle. Specifically, \(\cos \frac{\pi}{6} = \frac{\sqrt{3}}{2}\) and \(\tan \frac{\pi}{4} = 1\). Substitute these values into the expression and simplify.

We start by evaluating the trigonometric functions in the expression \(6 \cos \frac{\pi}{6} - 3 \tan \frac{\pi}{4}\). The known values are: \[ \cos \frac{\pi}{6} = \frac{\sqrt{3}}{2} \quad \text{and} \quad \tan \frac{\pi}{4} = 1 \]

Substituting these values into the expression gives: \[ 6 \cos \frac{\pi}{6} - 3 \tan \frac{\pi}{4} = 6 \left(\frac{\sqrt{3}}{2}\right) - 3(1) \]

Now, we simplify the expression: \[ = 6 \cdot \frac{\sqrt{3}}{2} - 3 = 3\sqrt{3} - 3 \]

Calculating the numerical value of \(3\sqrt{3} - 3\): \[ 3\sqrt{3} \approx 5.1961 \quad \Rightarrow \quad 5.1961 - 3 \approx 2.1961 \]

Final Answer