Precalculus Question of the Day

1. $\frac{\pi}{6}$ (correct answer)
2. $\frac{5\pi}{6}$
3. $\frac{\pi}{3}$
4. $\frac{7\pi}{6}$

Explanation: This question tests understanding of how the unit circle extends trigonometric functions to all real numbers. The reference angle is the acute angle formed between the terminal side and the nearest part of the x-axis, and it determines the magnitude of the trig values while the quadrant determines the sign. For angle θ = 7π/6 in Quadrant III, the reference angle is 7π/6 - π = π/6. Choice A is correct because it connects to the proper calculation for Quadrant III reference angle, subtracting π from the angle. Choice B uses the angle itself without finding the reference, but the reference is always acute and positive. The reference angle is always positive and acute, found by measuring to the nearest x-axis: for Quadrant II use π - θ, for Quadrant III use θ - π, for Quadrant IV use 2π - θ. Key to unit circle problems: first determine which quadrant the angle terminates in, then use the reference angle to find magnitudes, and finally apply the correct signs based on the quadrant (memorize: All Students Take Calculus for which functions are positive in each quadrant).