Determine the Quadrant on a Unit Circle
Answer 1
Olivia Lee
To determine the quadrant of the angle $( \theta )$ on the unit circle, we need to understand the angle’s position in relation to the x-axis and y-axis.
Consider the angle $( \theta = 150^{\circ} )$.
Step 1: Convert the angle to radians if needed. $( 150^{\circ} = \frac{5\pi}{6} )$ radians.
Step 2: Identify the reference angle and its position. Since$ \( 150^{\circ} \) $ is between$ ( 90^{\circ} ) and ( 180^{\circ} )$, it lies in the second quadrant.
Answer: The quadrant of$ ( 150^{\circ} ) $is Quadrant II.
Answer 2
Isabella Walker
Consider the angle $ ( heta = 240^{\circ} ) $.
Step 1: Convert the angle to radians if necessary. $ ( 240^{\circ} =\ frac{4pi}{3} ) $ radians.
Step 2: Recognize the reference angle and its location. Since$ ( 240^{\circ} )$ is between$ ( 180^{\circ} ) $ and $ ( 270^{\circ} ) $, it lies in the third quadrant.
Answer: The quadrant of ( 240^{circ} ) is Quadrant III.
Answer 3
Lily Perez
Consider the angle $ ( heta = 330^{circ} ) $.
Since $ ( 330^{circ} ) $ is between $ ( 270^{circ} ) $ and $ ( 360^{circ} ) $, it lies in the fourth quadrant.
Answer: The quadrant of $ ( 330^{circ} ) $ is Quadrant IV.
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