Defining the Unit Circle quiz #1 Flashcards
Defining the Unit Circle quiz #1
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How can you determine if a given point (x, y) is on the unit circle? To determine if a point (x, y) is on the unit circle, substitute its coordinates into the equation x² + y² = 1. If the equation is true, the point lies on the unit circle. What is the center of the unit circle on a coordinate plane? The center of the unit circle is at the origin, which is the point (0, 0). This means both the x and y coordinates of the center are zero. How are angle measures typically started and measured on the unit circle? Angle measures on the unit circle start from the positive x-axis at 0 degrees. They are measured counterclockwise around the circle. What is the radian measure for a full rotation around the unit circle? A full rotation around the unit circle is 2π radians. This is equivalent to 360 degrees. Which ordered pair corresponds to 90 degrees on the unit circle? The ordered pair for 90 degrees is (0, 1). This point is at the top of the unit circle. What is the equation of the unit circle and what does each variable represent? The equation of the unit circle is x² + y² = 1. Here, x and y represent the coordinates of any point on the circle. If a point has coordinates (a, b), what must be true for it to lie on the unit circle? The point (a, b) must satisfy the equation a² + b² = 1. If this equation holds, the point is on the unit circle. What is the x-coordinate of the point on the unit circle at 180 degrees? At 180 degrees, the x-coordinate is -1. The corresponding point is (-1, 0). How do you find the y-coordinate for a point on the unit circle at 270 degrees? At 270 degrees, the y-coordinate is -1. The point at this angle is (0, -1). What angle in degrees corresponds to the point (1/2, √3/2) on the unit circle? The point (1/2, √3/2) corresponds to 60 degrees on the unit circle. This is a standard reference angle.
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