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Trigonometric Functions on the Unit Circle definitions

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  • Unit Circle
    A circle with a radius of 1 centered at the origin, used to define trigonometric function values for all angles.
  • Trigonometric Functions
    Mathematical relationships connecting angles to coordinates on the unit circle, including sine, cosine, and tangent.
  • Sine
    The y-coordinate of a point on the unit circle corresponding to a given angle, representing the triangle's height.
  • Cosine
    The x-coordinate of a point on the unit circle corresponding to a given angle, representing the triangle's base.
  • Tangent
    A value found by dividing the y-coordinate by the x-coordinate on the unit circle; undefined when x equals zero.
  • Right Triangle
    A triangle formed by dropping a perpendicular from a point on the unit circle to the x-axis, with hypotenuse of length 1.
  • Hypotenuse
    The side of the right triangle on the unit circle that is always equal to the radius, which is 1.
  • Ordered Pair
    A set of x and y values representing a point on the unit circle, used to determine trigonometric function values.
  • Quadrant
    One of four regions in the coordinate plane, determining the signs of trigonometric values based on angle location.
  • Undefined Value
    A result occurring when division by zero happens, such as the tangent at 90 or 270 degrees on the unit circle.
  • Reciprocal
    A value obtained by inverting a fraction, used to simplify division when finding tangent values with fractional coordinates.
  • Numerator
    The top part of a fraction, especially relevant when dividing y by x to find tangent values on the unit circle.
  • Denominator
    The bottom part of a fraction, which, if zero, leads to an undefined tangent value on the unit circle.
  • Coordinate System
    A grid with x and y axes, providing the framework for locating points and determining trigonometric values.
  • Angle Measure
    A value, typically in degrees, that determines a point's location on the unit circle and its corresponding trigonometric values.