Unit Circle Diagram Quiz

Questions and Answers

The angle in radians corresponding to the point (1,0) is _____

2π

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 _____

π/4

What are the coordinates of the point at an angle of π/3 radians?

(1/2, √3/2) Signup and view all the answers

The angle in radians corresponding to the point (0,1) is _____

π/2 Signup and view all the answers

What is the angle in radians for the point (-1,0)?

π Signup and view all the answers

The coordinates for the angle 5π/6 radians are _____

(-√3/2, 1/2) Signup and view all the answers

What are the coordinates at an angle of 7π/6 radians?

(-√3/2, -1/2) Signup and view all the answers

The angle in radians corresponding to the point (0,-1) is _____

3π/2 Signup and view all the answers

What are the coordinates for the angle 11π/6 radians?

(√3/2, -1/2) Signup and view all the answers

Study Notes

Unit Circle Key Concepts

2π: 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.
2π/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.
3π/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.
5π/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.
7π/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.
5π/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.
4π/3: Represents 240 degrees; still within the third quadrant.
(-1/2, -√3/2): Coordinates for 4π/3, indicating negative cosine and negative sine values.
3π/2: An angle of 270 degrees; marks the bottom-most point on the unit circle.
(0,-1): Coordinates at 3π/2, signifying the lowest point with maximum negative sine.
5π/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.
7π/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.
11π/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.

Description

Test your knowledge of the unit circle with this fill-in-the-blank diagram quiz. Identify angles and coordinates associated with the unit circle in a fun and interactive way. Perfect for geometry or trigonometry students!