$Identify the Quadrants on the Unit Circle$
Answer 1
Matthew Carter
Given the angle θ = 45°, determine which quadrant of the unit circle the terminal side of the angle lies in.
Solve: First, convert the angle to radians if necessary. For 45°, the equivalent in radians is $ \frac{\pi}{4} $. Since $ \frac{\pi}{4} $ is a positive angle less than $ \frac{\pi}{2} $, it falls in the first quadrant.
Answer: The terminal side of the angle $ 45° $ lies in the first quadrant.
Answer 2
Olivia Lee
Given the angle θ = 135°, determine which quadrant of the unit circle the terminal side of the angle lies in.
Solve: First, convert the angle to radians if necessary. For 135°, the equivalent in radians is $ frac{3pi}{4} $. Since $ frac{3pi}{4} $ is a positive angle greater than $ frac{pi}{2} $ but less than $ pi $, it falls in the second quadrant.
Answer: The terminal side of the angle $ 135° $ lies in the second quadrant.
Answer 3
Mia Harris
Given the angle θ = 225°, determine which quadrant of the unit circle the terminal side of the angle lies in.
Solve: For 225°, the equivalent in radians is $ frac{5pi}{4} $. Since $ frac{5pi}{4} $ is a positive angle greater than $ pi $ but less than $ frac{3pi}{2} $, it falls in the third quadrant.
Answer: The terminal side of the angle $ 225° $ lies in the third quadrant.
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