Podcast
Questions and Answers
The angle in radians corresponding to the point (1,0) is _____
The angle in radians corresponding to the point (1,0) is _____
2Ï€
What are the coordinates of the point at an angle of π/6 radians?
What are the coordinates of the point at an angle of π/6 radians?
(√3/2, 1/2)
The angle in radians corresponding to the point (√2/2, √2/2) is _____
The angle in radians corresponding to the point (√2/2, √2/2) is _____
Ï€/4
What are the coordinates of the point at an angle of π/3 radians?
What are the coordinates of the point at an angle of π/3 radians?
The angle in radians corresponding to the point (0,1) is _____
The angle in radians corresponding to the point (0,1) is _____
What is the angle in radians for the point (-1,0)?
What is the angle in radians for the point (-1,0)?
The coordinates for the angle 5Ï€/6 radians are _____
The coordinates for the angle 5Ï€/6 radians are _____
What are the coordinates at an angle of 7Ï€/6 radians?
What are the coordinates at an angle of 7Ï€/6 radians?
The angle in radians corresponding to the point (0,-1) is _____
The angle in radians corresponding to the point (0,-1) is _____
What are the coordinates for the angle 11Ï€/6 radians?
What are the coordinates for the angle 11Ï€/6 radians?
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Study Notes
Unit Circle Key Concepts
- 2Ï€: Represents a full revolution around the unit circle, equivalent to 360 degrees.
- (1,0): The coordinates for the point on the unit circle at an angle of 0 radians (0 degrees).
- π/6: An angle measuring 30 degrees; identifies a specific location on the unit circle.
- (√3/2, 1/2): Coordinates corresponding to the angle π/6; reflects the cosine and sine values at this angle.
- π/4: An angle of 45 degrees; significant for its equal cosine and sine values.
- (√2/2, √2/2): Coordinates for the angle π/4, indicating equal values for sine and cosine.
- π/3: Represents an angle of 60 degrees; important for its relationship with the unit circle.
- (1/2, √3/2): Coordinates for the angle π/3, showcasing the cosine and sine ratios at this angle.
- π/2: An angle of 90 degrees; signifies the topmost point on the unit circle.
- (0,1): Represents the coordinates at 90 degrees, where the sine value is maximum.
- 2Ï€/3: An angle of 120 degrees; part of the second quadrant on the unit circle.
- (-1/2, √3/2): Coordinates for the angle 2π/3, indicating negative cosine and positive sine.
- 3Ï€/4: Corresponds to 135 degrees, an angle located in the second quadrant.
- (-√2/2, √2/2): Coordinates for 3π/4, reflecting negative cosine and positive sine.
- 5Ï€/6: An angle of 150 degrees; identified with the second quadrant.
- (-√3/2, 1/2): Coordinates at 5π/6, showing negative cosine and positive sine.
- π: Represents 180 degrees, a pivotal angle on the unit circle.
- (-1,0): Coordinates at π; indicates a full transition to the negative x-axis.
- 7Ï€/6: An angle of 210 degrees; situated in the third quadrant.
- (-√3/2, -1/2): Coordinates for 7π/6, demonstrating both negative sine and cosine.
- 5Ï€/4: An angle of 225 degrees; also in the third quadrant.
- (-√2/2, -√2/2): Coordinates corresponding to 5π/4, highlighting equal negative sine and cosine.
- 4Ï€/3: Represents 240 degrees; still within the third quadrant.
- (-1/2, -√3/2): Coordinates for 4π/3, indicating negative cosine and negative sine values.
- 3Ï€/2: An angle of 270 degrees; marks the bottom-most point on the unit circle.
- (0,-1): Coordinates at 3Ï€/2, signifying the lowest point with maximum negative sine.
- 5Ï€/3: An angle of 300 degrees; found in the fourth quadrant.
- (1/2, -√3/2): Coordinates for 5π/3, reflecting positive cosine and negative sine.
- 7Ï€/4: Corresponds to an angle of 315 degrees; also in the fourth quadrant.
- (√2/2, -√2/2): Coordinates for 7π/4, indicating equal negative sine and positive cosine.
- 11Ï€/6: An angle of 330 degrees; positioned close to the full rotation.
- (√3/2, -1/2): Coordinates for 11π/6, highlighting positive cosine and negative sine.
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