Solved examples of angles in standard position with diagrams

📚 Quick Study Guide

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• Standard Position: An angle is in standard position if its vertex is at the origin (0,0) and its initial side lies along the positive x-axis.
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• Positive Angles: Measured counter-clockwise from the initial side.
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• Negative Angles: Measured clockwise from the initial side.
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• Coterminal Angles: Angles that share the same terminal side. To find coterminal angles, add or subtract multiples of $360^\circ$ (or $2\pi$ radians).
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• Quadrantal Angles: Angles whose terminal side lies on the x-axis or y-axis (e.g., $0^\circ$, $90^\circ$, $180^\circ$, $270^\circ$, $360^\circ$).
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• Reference Angle: The acute angle formed by the terminal side of the angle and the x-axis.

📝 Practice Quiz

1. What quadrant does an angle of $210^\circ$ lie in when in standard position?
   1. Quadrant I
   2. Quadrant II
   3. Quadrant III
   4. Quadrant IV
2. An angle of $-45^\circ$ in standard position terminates in which quadrant?
   1. Quadrant I
   2. Quadrant II
   3. Quadrant III
   4. Quadrant IV
3. What is a coterminal angle to $60^\circ$?
   1. $-60^\circ$
   2. $-300^\circ$
   3. $120^\circ$
   4. $240^\circ$
4. Which of the following is a quadrantal angle?
   1. $45^\circ$
   2. $60^\circ$
   3. $90^\circ$
   4. $120^\circ$
5. What is the reference angle for $150^\circ$?
   1. $30^\circ$
   2. $60^\circ$
   3. $150^\circ$
   4. $210^\circ$
6. An angle measuring $\frac{5\pi}{4}$ radians lies in which quadrant?
   1. Quadrant I
   2. Quadrant II
   3. Quadrant III
   4. Quadrant IV
7. What is the measure of an angle that is coterminal with $\frac{\pi}{2}$?
   1. $\frac{-\pi}{2}$
   2. $\frac{3\pi}{2}$
   3. $\frac{5\pi}{2}$
   4. $\frac{7\pi}{4}$