Exploring the Unit Circle in Algebra II

What is the radius of the unit circle?

• √2 units

• 1 unit

• 2 units

• π units

Which equation represents the unit circle?

• x^2 + y^2 = 2

• x^2 - y^2 = 1

• x^2 + y^2 = 1

• x^2 + y^2 = 0

What is the length of the side opposite the 45° angle in a 45-45-90 triangle with hypotenuse 1?

• √2/2

• 1/√2

• 1/2

• √3/2

In a 30-60-90 triangle, what is the length of the side opposite the 30° angle, if the hypotenuse is 1?

• 1

• 1/2

• √3/2

• √2/2

What are the coordinates of the point on the unit circle at 90°?

• (0, 1)

• (1, 0)

• (-1, 0)

• (0, -1)

What are the coordinates of the point on the unit circle at 45°?

• (√2/2, √2/2)

• (1/2, √3/2)

• (√3/2, 1/2)

• (1, 0)

How are the coordinates of points in the second quadrant related to those in the first quadrant?

• x-coordinate is negated

• y-coordinate is negated

• Both coordinates are negated

• Coordinates remain the same

What is the significance of the unit circle in trigonometry?

• It defines the sine and cosine for angles greater than 180°

• It is only relevant for angles of 90° and 270°

• It is used to calculate the area of circles

• It helps in solving linear equations

What does a negative angle, like -120°, indicate in terms of its position on the unit circle?

• It is always located in the fourth quadrant

• It cannot have a corresponding point on the unit circle

• It is coterminal with an angle greater than 360°

• It represents an angle measured clockwise from the positive x-axis

How can the sine and cosine functions be defined using the unit circle?

• Through the circle's diameter

• Using the circle's circumference

• By the coordinates of points on the circle

• Based on the circle's area