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Sum and Difference Identities definitions

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  • Sum and Difference Identities
    Formulas that express trig functions of sums or differences of angles in terms of functions of individual angles.
  • Sine Sum Identity
    Formula expanding the sine of a sum into products of sines and cosines of the individual angles.
  • Sine Difference Identity
    Formula expanding the sine of a difference into products of sines and cosines of the individual angles, with a sign change.
  • Cosine Sum Identity
    Formula expressing the cosine of a sum as the difference of products of cosines and sines of the angles.
  • Cosine Difference Identity
    Formula expressing the cosine of a difference as the sum of products of cosines and sines of the angles.
  • Tangent Sum Identity
    Formula expressing the tangent of a sum as a quotient involving the tangents of the individual angles.
  • Tangent Difference Identity
    Formula expressing the tangent of a difference as a quotient involving the tangents of the individual angles, with sign changes.
  • Unit Circle
    A circle of radius one centered at the origin, used to define exact values of trig functions for standard angles.
  • Quadrant
    One of four regions in the coordinate plane, used to determine the sign of trig values based on angle location.
  • Cofunction Identity
    Relationship showing how trig functions of complementary angles are related, often verified using sum and difference identities.
  • Verification
    Process of simplifying one or both sides of a trig equation to show equality, often using identities.
  • Pythagorean Theorem
    Relationship among the sides of a right triangle, used to find missing side lengths when solving trig problems.
  • Exact Value
    A non-decimal, simplified result for a trig function, often involving radicals or fractions, not approximated numerically.
  • Special Right Triangle
    A triangle with angle measures and side ratios that are commonly used to quickly find trig values.
  • Argument
    The angle or expression inside a trig function, which may be a sum or difference of two angles.