Which of the following statements shows how to calculate the reference angle for \( \theta=\frac{11 \pi}{6} \) ? \( \begin{array}{l}\pi-\theta \\ \theta-\pi \\ 2 \pi-\theta \\ \text { DONE }\end{array} \)
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Mind Expander
To find the reference angle for \( \theta = \frac{11 \pi}{6} \), it's important to note that this angle lies in the fourth quadrant. The reference angle is determined by subtracting the angle from \( 2\pi \) since it is greater than \( \pi \). Thus, we calculate it using the formula \( 2\pi - \theta = 2\pi - \frac{11\pi}{6} = \frac{\pi}{6} \). A common mistake when calculating reference angles is to confuse the quadrants and apply the wrong formulas. Remember, angles in the first quadrant simply retain their value, angles in the second quadrant use \( \pi - \theta \), in the third quadrant it's \( \theta - \pi \), and in the fourth quadrant, like here, it's \( 2\pi - \theta \). Stay sharp with those quadrant rules!
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