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Trigonometric Functions on the Unit Circle definitions

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  • Unit Circle
    A circle with radius 1 centered at the origin, used to relate angles to coordinates and trigonometric values.
  • Trigonometric Functions
    Mathematical relationships connecting angles to coordinates, specifically using sine, cosine, and tangent.
  • Sine
    The y-coordinate of a point on the unit circle corresponding to a given angle, representing triangle height.
  • Cosine
    The x-coordinate of a point on the unit circle for a given angle, representing triangle base.
  • Tangent
    A value found by dividing the y-coordinate by the x-coordinate for a given angle on the unit circle.
  • Right Triangle
    A geometric figure formed by connecting the origin, a point on the unit circle, and the x-axis.
  • Hypotenuse
    The side of a right triangle on the unit circle, always equal to the radius, which is 1.
  • Quadrant
    One of four regions in the coordinate plane, affecting the sign of trigonometric values.
  • Ordered Pair
    A set of x and y values representing a point on the unit circle, used to determine trig values.
  • Undefined Value
    A result from dividing by zero, such as tangent at 90 or 270 degrees, which cannot be calculated.
  • Reciprocal
    A value obtained by swapping the numerator and denominator, used in fraction division for tangent.
  • Negative Value
    A trig result occurring in certain quadrants, reflecting the sign of coordinates on the unit circle.
  • Degree Measure
    A way to specify angles, such as 0, 60, 90, 180, 217, or 270, for locating points on the unit circle.
  • Base
    The horizontal side of a right triangle on the unit circle, matching the x-coordinate.
  • Height
    The vertical side of a right triangle on the unit circle, matching the y-coordinate.